ES 13 ProbSet 1

PROBLEM SET 1: STRESSES

1. Find the maximum allowable value of P for the column. column. The cross-sectional areas and working working stresses (σw) are shown in the figure. 2. Determine the mass of the heaviest uniform uniform cylinder that can be supported in the position position shown without exceeding a stress of 50 MPa in cable cable BC. Neglect friction and the weight of the bar AB. The cross-sectional 2

area of BC is 100 mm . 2

3. The cross-sectional of of each member of the truss is 1.8 in . Calculate the stresses in mebers CE, DE, DE, and DF. Indicate tension or compression.

4. A key prevents relative rotation rotation between the shaft and the pulley. If the torque T=2200 T=2200 N-m is applied applied to the shaft, determine the smallest safe dimensions b if the working shear stress for the key is 60 MPa. 5. For the joint shown, calculate (a) the largest bearing stress between the pin and the the members; (b) the average shear stress in the pin; and (c) the largest average normal stress in the members. 6. The steel end-cap is fitted fitted into grooves cut in the timber timber post. The working stresses for the post are 1.8 1.8 MPa in shear parallel to the grain and 5.5 MPa in bearing bearing perpendicular to the the grain. Determine the smallest safe safe dimensions a and b.

7. A triple-riveted lap joint unites two 12-mmmm plates. The rivets are 25 mm in diameter and are spaced 150 mm in the outer rows and 75 mm in the inner row. When the tensile stress is 100 MPa in the gross section of the plate, determine; (a) the average intensity of the shearng stress in the rivets; (b) the average bearing stress on the plates; (c) the highest average tensile stress, and state where it occurs. 8. A cylindrical compressed air tank with an inside diameter of 900 mm is made of 10-mm plate and is subjected to internal pressure of 2 MPa. The longitudinal seam is double-riveted butt joint with a 6=mm cover plates. The 20-mm diamter rivets in 22-mm holes are spaced at 60 mm in the inner rows and 120 mm in the outer rows. Determine (a) the average shearing stress in the rivets; (b) the highest average bearing stress between the rivets and any plate; (c) the highe st average tensile stress in the plates, and state where it occurs. 9. Each of the two vertical links CF connecting the two horizontal memebres AD and EG has a 10 x 40 mm uniform rectangulaer cross section and is made of a steel with an ultimate strength in tension of 400 MPa, while each of the pins at C and F has a 20-mm diamter and is made of a steel with an ultimate strength in shear of 150 MPa. Determine the overall factor of safety for the links CF and the pins connecting them to the horizontal members. 10. In the steel structure shown, a 6-mm-diamter pin is used at C and 10-mm-diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that the factor of safety of 3 is desired, determine the largest load P that can be applied at A. Note that link BD is not reinforced around the pin holes.