1. For the Pratt bridge truss and the loading shown below, determine the average normal stress in member BE, knowing that the cross-sectional area of that member is 60 in². 9:0 E 26-12--12--12--- 50 kips 50 kips 50. Lips Figure 1 JULIO

If the material in the previous problem was found to have a plane strain fracture toughness of KIC = 37 MPa√m, and a yield strength of 400 MPa, would the plate fail first by brittle fracture or plastic yielding? Why?

Two wood beams each with an actual cross section of 2 X 4 in are loaded as shown. If there is light contact between the beams prior to load application, determine the support reactions after the 500-lb force is applied. Assume that only a vertical force is transmitted between the beams at point B.

The steel beam ABCD shown is supported at C as shown and supported at B and D by steel bolts each having a diameter of 8 mm. The lengths of BE and DF are 50 and 60 mm, respectively. All dimensions are given in millimeters. Prior to loading, the nuts are just in contact with the beam, which is horizontal. A force of 2 kN is applied at point A. For steel, E = 209 GPa. Determinethe stresses in the cables and the deflections of points A, B and D if (a) beam ABCD is considered to be rigid, and (b) beam ABCD is elastic with a second area moment of I = 200 mm^4

The steel beam ABCD shown is simply supported at A and supported at B and D by steel cables each having a diameter of 12 mm. A force of 20 kN is applied at point C. For steel E = 209 GPa. Determine the stresses in the cables and the deflections of points B, C and D if (a) Beam ABCD is considered to be rigid (b) Beam ABCD has a second-area moment of I = 800,000 mm².

Each of the three solid steel shafts has a diameter of 20 mm. Shafts AB and EF are 600 mm long, whereas shaft CD is 300 mm long. The pitch radii of gears B, C, and F are 30, 80 and 50 mm, respectively. For steel E = 200 GPa and v=0.3. If torque of 10 N.m is applied to shaft AB as shown, determine the shear stresses in each shaft and the angle through which each gear rotates.

This figure shows a plate, with a hole at its centre, being subject to a tensile test. A constant pressure,, is applied to the left-most and right-most surfaces of the plate. The plate is made from steel: Given: 50 163 1000 400 1

Lame’s problem (annular region of radii a and b with internal and external pressure P1 and P0 was treated in class. The stress function for this problem was given in class as

Axial loads are applied with rigid bearing plates to the solid cylindrical rods shown in the figure. The diameter of aluminum rod (1) is 2.00 in., the diameter of brass rod (2) is 1.75 in., and the diameter of steel rod (3) is 3.00 in. Determine the axial normal stress in each of the three rods. Assume P = 8 kips, Q = 4 kips, R = 10 kips and S= 21 kips. The normal stress is positive if tensile and negative if compressive.

2. A 1/8" radius steel rod that is 2 ft long has a 20,000 in-lbs external torque applied. [J = (T4)/2] A. What is the polar moment of inertia for the rod? B. If the Modulus of Rigidity for the steel bar is 18 X 10³ Ksi, what is the expected twist of the bar in degrees?