Example 1 (Adopt Test 2 March 2010) Figure Q1 shows a pin-jointed truss with loads 22.7 kN and 45 kN applied at joint A. In addition to the load shown, member AB was found fabricated 5 mm too short.
a) Form the global stiffness relations corresponding to the unconstrained degrees of freedom and solve for the non-zero degrees of freedom. b) Analyse for the axial forces in members 1 and 3 if, the structure is still acted upon by the 22.7 kN load (without the 45 kN load) and member AB was considered cut to the right length (no fabrication error). Given A Given A = = 322 mm 2 for all members in the pin-jointed truss and E and E = = 200 GPa
D
45 kN
6m
1
22.7 kN A
6m 2
3
B
C
9m
9m
Figure Q1 Learning Outcomes:
This test is designed to access student ability’s on:
able to identify and number the unconstrained degree of freedoms of the indeterminate truss and able to determine the non-zero degrees of freedom.
able to establish the element stiffness matrices of all members in global coordinate system.
able to assemble the structure stiffness equation
able to determine the axial forces for the given members using the element stiffness matrices and force vectors.
ECS468 (INDETERMINATE (INDETERMINATE STRUCTURES)
4
Solution:
3 D
45 kN
6m
1
2
1 22.7 kN A
6m 2
6
B
8
3
5
C
9m
7
9m
Figure Q1
a) Form the global stiffness relations corresponding to the unconstrained degrees of f reedom and solve for the non-zero degrees of freedom. (CO2-PO3)
Du
D1 = ? D2 = ?
Dk
D3 = 0 D4 = 0 D5 = 0 D6 = 0 D7 = 0 D8 = 0
Qu
Q3 = ? Q4 = ? Q5 = ? Q6 = ? Q7 = ? Q8 = ?
Qk
Q1 = 22.7 Q2 = - 45
ECS468 (INDETERMINATE (INDETERMINATE STRUCTURES)
Member Stiffness Matrix
C x2 AE C x C y k 2 L C x C x C y
c) Analyse for the axial forces in members 1 and 3 if, the structure is still acted upon by the 22.7 kN load (without the 45 kN load) and member AB was considered cut to the right length (no fabrication error). (CO2-PO3)
c) Analyse for the axial forces in members 1 and 3 if, the structure is still acted upon by the 22.7 kN load (without the 45 kN load) and member AB was considered cut to the right length (no fabrication error). (CO2-PO3)
