Samplex LE1

E.S. 13 - Mechanics of Deformable Bodies

1st Semester, A.Y. 2010-2011

LONG EXAM 1 4:00-6:00 PM July 5, 2010 Instructions: 1. 2. 3. 4. 5. 6.

Start each problem on a new page and do not write at the back Be sure to write your name, student number and section on each page of your answer sheet Use only a blue or a black ink pen. Do not use correction fluid for erasures. Show clearly your complete solution and state, if any, the assumptions made. Any form of cheating will be strictly penalized. Take a biological break before the exam as no one will be allowed to leave the examination room for the entire duration of the exam. 7. Turn off celphone and other communication devices.

Problem 1. A square plate in Figure 1 has the following dimensions before normal stresses are applied: Lx = Ly = 160 mm, t=20 mm. Its Poisson’s ratio, ν = 0.283, and its modulus of rigidity, G = 30 GPa. It is then subjected to normal stresses on ALL its faces and deforms. a) If the normal stresses are σx = 444 MPa, σy = 222 MPa, and its new length along the xdirection is 160.8437 mm, find σz. b) Find the new thickness of the plate, t’. c) Find the new length along the z - direction, Lz’.

Figure 1

P Problem 2. Member A of the timber step joint for a truss is subjected to a compressive force P(kN) as shown in Figure 2. The ultimate stress of the steel material used in the hanger rod C is 470 MPa while the maximum shear stress in wood B is 30 MPa. Determine the maximum allowable force P if the Factor of Safety against failure by shearing of B is 3 and the Factor of Safety against failure by fracture of C is 2.5. The steel rod C has a diameter of 10 mm and the wood B has a width of 30 mm. Note: Neglect bearing of rod C on wood B.

FC C

A

Figure 2 60O

FB

B Shear Failure surface 40 mm

Problem 3. The steel system in Figure 3 deformed as shown due to the load P. There is a 0.15 mm clearance in member B at its connection with rigid member C. The maximum strains in members A, B, and D are 3.33 x 10-4, 9.00 x 10-4, and 1.58 x 10-4 respectively due to the said loading. Deformation of the square plate E was due to shear forces (as illustrated in the isolated figure) and each side of the plate also elongated with a maximum strain of 1.25 x 10-7. (E = 200 GPa, G = 83 GPa) a). Calculate the shear strain in plate E. b). Determine the maximum displacement of point b due to the loading. c). Compute for the expected value of lateral strain in member B.

Figure 3