Chapter 1.5, Problem 68P

Solve the preceding problem for a plate of dimensions 100 mm × 250 mm subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction (see figure).

Solve the preceding problem for sx= 11 MPa and ??y= -20 MPa (see figure).

-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.

A suspender on a suspension bridge consist of a cable that passes over the main cable (see figure) and supports the bridge deck, which is Far below. The suspender is held in position by a metal tie that is prevented from sliding downward by clamps around the suspender cable. Let P represent the load in each part of the suspender cable, and let represent the angle of the suspender cable just above the tie. represent the allowable tensile stress in the metal tie. (a) Obtain a formula for the minimum required cross-sectional area of the lie. (b) Calculate the minimum area if P = 130 kN, = 75°, and allow=80 .

A post AB supporting equipment in a laboratory is tapered uniformly throughout its height H (see figure). The cross sections of the post are square, with dimensions b × b at the top and 1.5b × 1.5b at the base. Derive a formula For the shortening 8 of the post due to the compressive load P acting at the top. (Assume that the angle of taper is small and disregard the weight of the post itself.)

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.

An aluminum tube has inside diameter dx= 50 mm, shear modulus of elasticity G = 27 GPa, v = 0.33, and torque T = 4.0 kN · m. The allowable shear stress in the aluminum is 50 MPa, and the allowable normal strain is 900 X 10-6. Determine the required outside diameter d2 Re-compute the required outside diameter d2, if allowable normal stress is 62 MPa and allowable shear strain is 1.7 X 10-3.

Solve the preceding problem if the mass of the tailgate is MT— 11 kg and that of the crate is hic— 6S kg. Use dimensions H = 305 mm, L = 406 mm, dc= 460 mm, and dT= 350 mm. The cable cross-sectional area is At= 11.0 mm'. (a) Find the tensile Force T and normal stress T in each cable. (b) IF each cable elongates

The nonprismalic cantilever circular bar shown has an internal cylindrical hole of diameter dtl From 0 to x so the net area of the cross section n for segment I is A. Load P is applied at x, and load Ptl is applied at x = L. Assume that E is constant. (a) Find reaction force Ry (b) Find internal axial forces Ntin segments I and 2. (c} Find .v required to obtain axial displacement at joint 3 of