x = A cylindrical rod is made of three segments and is subjected to axial loads as indicated in the figure. The diameters of the segments are : 0.5 in, y = 1 in, and z = 0.5 in. Find the average normal stress at points A, B, and C. Remember that the sign convention is tension positive, and compression is negative. 3 kip A 9 kip у Z BY NO SA B 2021 Cathy Zuple C 8 kip 2 kip The average normal stress at A is σ A = The average normal stress at B is σ = The average normal stress at C is σc = ksi. ksi. ksi.

Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.

A steel punch consists of two shafts: upper shaft and lower shaft. Assume that the upper shaft has a diameter d1= 24 mm and the bottom shaft has a diameter d2= 16 mm. The punch is used to insert a hole in a 4 mm plate, as shown in the figure. If a force P - 70 kN is required to create the hole, what is the average shear stress in the plate and the average compressive stress in the upper and lower shaft of the punch?

The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?