mekanika kekuatan material

  





                                                                                 

    

    

    

    

    

    

    

    

    

    

    

    

    

     

                                                                                                                                                                                                                                                                                                                                  

    

                                                                                                                                                                       

   



       

  



  









                                                                                                                                           



                           



   

  









                                                                           

                                                          

      









      

                                                                                                

      

      

    

                                                              

    

     

                                

    

   

   

   

   

   

   

   



 

 

                                                  

 

              

             

               

         



     

                    



             

 



  

                

         



      

        

                       

            

       



                                   

       



  







                                       

                                                                            



             

                                             



     

                                       

 

   















    

    



          

   



             

      



                                                                                             



     

 

                                                 

    

                 

                        



   

                 

                                                                                                          

                                                 

               

        

                      

                                              

  



                                         



      

      

  



     



   



 

    

   

   

     

   

     

  

                                      

       

                                    



   

   

                            

                              

     





   

  

   





   



   





    











    



          

  



                         

 















  









       



  

 





 

  

 





    

















        

                                       



   

                                      

 

   



  





 





  

   

 

 



 

  

     

  



    

                                    

   



                  

     

 

  



    





                                                





    











     





                                   

 

                        

  



         

                                           

 



   

 

     

 

     





 

     





 

     

    



                   







       



       



 

    









   

  

 





 



  

 

















 



 



  

    





  



                                 

    

                                    

              

   









                        

   

                   













   







    



   

            

   













     

  









 







   

 







 



















 





 





 



 





                                             

 

   





      

 

                                             

   



     

   

                                            

 

 

   



   

                              



   

                                 



                                                                   







                       













                     

                       

       

 



  

   

               

       



      

     

       

               

                                                                   





 









     







                                    



   

 

 









      

                                            



            







          



















     













 

                              

         

  



    





        

      



                                                                                                                                              

 

                                                                   

                                                   

                                  



                           

                           

            

                                      

             

                        

 

                   

 



     

 



    























   



 



       













 







 

                                                                               





  







     



  



     







                                                 



     

 

    

   



                          



 



     

     

                    

                                      

 

                    

    

         

 

  

                       

 

      

 

       

                

                                                

                             

              

 



 

    

        



     



 

 

 



     



 





    



 

  



 



 

 

 





  

 







 











 

   



    

 

 

       















 

 



 

 



   

 

 



                 

   



     







                                           

           

       

            

  

 

 

       

 

    

 

  

     





         

     









       

           

                                       

               



     

       



 

      



 

        

 



 

 



 







     

 



    









  

 



 











  

 



  

 

       







 











  





  





   

  

 

    

 



 

                          

         

                    

 

                   

                            

                     

       

 

      

 

       

 

         



 

 





     

     

 







 





    







 

















 





 







   



  

 

 

 

 



       



 

 







 



   

 

     











 



 



   







   



 

    

 



 

  

                           



 



 

 



 





         

 

 





                             









   





 











        







 

  









                     



 







 

 



















 

 





 



 





   





 







 





















 









     



















































 























 









                                               

       

      



                     











 





 



        







 





 

     

   

 

  

 



 

     

       













 

 

         

 

       



 

                      

                                

                         

       



 

      



 





 

    

       



 



              







 



 



 

 





     



 









 



 







    







 

 























    

  



  





 

 



 

 



 

















  

 













   



       



 

 







 



   

 

  









 













   







   



 

  



  

  

 

 



     

  

                 

          

        

 



 

 



 









 



                               







     







   





        







     









 

   



                     





 

   

 



 

  

 

  





  





     





 



 



  

 



  





  



 









 





   









   

 







  



 

  

 







 





  

 

 











  



  

 



  













                                                               

          

  



       





 

 

    

 

 



 





 

     

  





 

 

 

 



         



            







 





 



 

 

     

                                                                           

        

       



 

 











               



  

  



  

 









             



      

  



     





     

 







 



    

     





  



 



   





  

        







 



    





      

 

  

                                                                                              

         

 

                                      

  

             

                                                                                           



                                                                        

 

                                                  

 

          

                                

                                                                                                                                                    

                                               

       



     

              

                                                                                                                                                                             

                                                     

         

  

                         

                                                                                                                                                                                                                                                



     

   

       

            

                                              

 

                                                                                                                                                                                                  

                                                                     

  

                                



     

                                                                                                                                                                                                                         

                                                           

         

                             

                 

                                                                                                                                                       



                                                                                 

                                                                                             

                                                                                                                                               



     

 

                           

    

                                

     



   

 





















  















         





        











                    





               

         





















                            

                                               

       

                  

                                 

          

  



     



             





    

       

 



  























                     

                              

                 





                         

        

         

                                         





            





















     











                  



















         





                         



   





 





                 







   







      















                         











      





 



























                 

        

                                           







               









              





                                          





                               



  



    



   













           



 









 











        











         

















               









                        

                                 













 

    



        



      

















  







 











     













         















                

  























   











































 



   





  







  

    

    



  







  







   





 







 











   

        







 





 















                                                   

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      

  

  



 

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  



  

 



                             

 

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 

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

 

  

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 

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   

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                 

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                    



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     

  





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

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

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 

















  



  



 

   

   



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





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





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



 

  





















          

 













             

 











 





 

  







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

    



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

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

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 

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     



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                                               



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

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 

        

                                      

        



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

                 







 

 







     















                     



































 







      









                      



 





                 





     



   









                             















 

   



  



       

























              













 

 





 



                                                       

 

  

 

             

  

  

 

   



        

         

                                       









               















 









     















     





                                





 





 



















  

       















   





                          







     



 





                

 



        





 



 







 











      











  







 



 

      





  









 

       

 

   

   







  

    

                                                                    

 

   





        



                                                                                 

  

 

                            

                      

  





     

    







         





   





















        







                               



 







                          







                    





























 





      



















 









            





 





        

                                                                    









    

 

     







                  

        

                                                                 

 





          

 





 

 



     













 













 



 





 

 









 

                     

  

                                  

 



 



 



   

        

 

                                   





 



 

                                        

     



    

















     

     







         



















        







                        



 







      







                  





   



























      































          



 





            



























                                                       







            









            

       

       

                                                                  

 





       



 



 

 



    



















 







 



 





 

 

  







                           

  



   

                                    

 

 



 

  





       

   

 

      



 





     



 

 

   

   

 

       

     

                           

                                     

     



 

                        

                           

 

                                      

 

   









   

 



   



  











                                  



















  

 

                                          

       

       

                                            



 









       



 





      



    

            





















 







                            



 





     





                   













































 

             





 





                                 



   

                           

 

    







       













       

 

   

 

   

              



    



              

  

                                                     

  



   

 

 

                                                                                        

                                                                  

 

 



      

         

    

    

  

           

     

   

 

                                      





        





           









                      

        

                                                



 









        



 





 







   





 







 





                              



      





 









                                                     

















            



            

                                          





         





 



                  



 





       

           





 





                                   



 



 

 





  

















    





























      

                  

        

















                    



















 

















              





       



  







 







 







 

  











   





  



                              

  

                               

       



 



 

              

  

 





 







    

 

 



            

  

 

 

   

  







  

 

 

  



     

        

    



      

                           





          









            











                      





 











          





 











     





















             



 







            



 





 

 







 





          



 

  



 











 



              

                          













       

    





 

          

                                             









         









           













      

                    



 











      



 











                                      

        











 

 



 



















 





       



 



 









 





 











                       





 















    







 

 





 















  

 



 





 







 



    

 



   

 



                                



      

                              







    

       

  



 







 

          

        

                                                     

 







         

       

 















 

 









              

     

                          















   





        

   

       

                                                               

 

 



 



         



  





      

      









 



  

 







 

  











                                                                   

 

 



 

 





             

 

              

  



 

 

        

 

         

     



     

                                                        



    



         



  







 







 







                             



      

                             















    

         



 

 

   



 

 

         

 

   

       

                           

      



                               



    



         



  







 







 









        

            

  

                 

  

               

                                  

