Question

(MPa) 3 kip 3 kip 2 kip 2 kipi 2 kip --5--5-+-5ft + } } } } 490 75114 } HE € (mm/mm) A Fig. for Q.1 OLO Fig. for Q.2 1. Determine the size of the square bearing plates A and B required to support the loading. Assume all the loads on the beam as dead load. Use the LRFD method. Assume the resistance factor = 0.9 and dead load factor as 1.4. The failure stress is 500 psi. 20 Points 2. The elastic portion of the stress strain diagram for an aluminum alloy is shown in the figure. The specimen from which it was obtained has an original diameter of 15 mm. The gauge length is 60 mm. When the applied load on the specimen is 50 kN, the diameter is 14.9749 mm. Determine Poisson's ratio for the material. 15 Points

Answer 1

2 diagram, find modulus of from the elasticity stress - strain of Aluminium 490 - 0.007 70000 MPa € Original diameter of sample d = 15 mm Original cross section area of the sample A = 1/4 = 1 15% = 176.41 mm . Normal stress = = - - 50x103 - 282.9 MPa find longitudinal strain 4. 176.71 E o - 282.9. Tong Ent = 4.8414 x 10 70000 mm/mm Diameter of sample after applying the load final diameter a de = 19.9749 mm Difference in diameter before and after of application load = Ad = dor do - 14.9749-15 = – 0.0251 mm lateral strain = at Ad =0.3575-1673x10 mm laims Poisson's natio=ver Flat Elong - 12673x10 3 4.00 14x10 3 = 0.414