Exam 7: Tension, Compression and Shear

steel wire hangs from a high-altitude balloon. The steel has unit weight of 77 kN/m $77 \mathrm { kN } / \mathrm { m } ^ { 3 }$ and yield stress of 280 MPa. The required factor of safety against yield is 2.0. The maximum permissible length of the wire is Approximately:

titanium bar ( $( E = 100 \mathrm { GPa } , v =0.33 ) \text { with square cross section } ( b = 75 \mathrm {~mm} ) \text { and length } L = 3.0 \mathrm {~m} \text { is }$ subjected to tensile load P = 900 kN. The increase in volume of the bar is approximately:

hollow circular post ABC (see figure) supports a load $P _ { 1 } = 16 \mathrm { kN }$ 16 kN acting at the top. A second load $P _ { 2 }$ is uniformly distributed around the cap plate at B. The diameters and thicknesses of the upper and lower parts of the post are $d _ { A B } = 30 \mathrm {~mm} , t _ { A B } = 12 \mathrm {~mm} , d _ { B C} = 60 \mathrm {~mm} , \text { and } t _ { B C } = 9$ 9 mm, respectively. The lower part of The post must have the same compressive stress as the upper part. The required magnitude of the load $P _ { 2 }$ is Approximately:

aluminum bar $( E = 72 \mathrm { GPa } , \nu = 0.33 )$ of diameter 50 mm cannot exceed a diameter of 50.1 mm when compressed by axial force P. The maximum acceptable compressive load P is approximately:

aluminum bar ( $( E = 70 \mathrm { GPa } , v = 0.33 )$ 0.33) of diameter 20 mm is stretched by axial forces P, causing its diameter to decrease by 0.022 mm. The load P is approximately:

Two flanged shafts are connected by eight 18-mm bolts. The diameter of the bolt circle is 240 mm. The allowable shear stress in the bolts is 90 MPa. Ignore friction between the flange plates. The maximum value of $90 \mathrm { MPa }$ torque $T _ { 0 }$ is approximately:

$\text { A pipe } \left( E = 110 \mathrm { GPa } \text { ) carries a load } P _ { 1 } = 120 \mathrm { kN } \text { at } A \text { and a uniformly distributed load } P _ { 2 } = 100 \mathrm { kN } \right. \text { on }$ the cap plate at $B$ . Initial pipe diameters and thicknesses are $d _ { A B } = 38 \mathrm {~mm} , t _ { A B } = 12 \mathrm {~mm} , d _ { B C } = 70 \mathrm {~mm}$ , and $t _ { B C } = 10 \mathrm {~mm}$ . Under loads $P _ { 1 }$ and $P _ { 2 }$ , wall thickness $t _ { B C }$ increases by $0.0036 \mathrm {~mm}$ . Poisson's ratio $v$ for the pipe material is approximately:

steel plate weighing 27 kN is hoisted by a cable sling that has a clevis at each end. The pins through the clevises are 22 mm in diameter. Each half of the cable is at an angle of 35° to the vertical. The average shear $35 ^ { \circ }$ stress in each pin is approximately:

polyethylene bar ( $( E = 1.4 \mathrm { GPa } , v = 0.4 )$ 0.4) of diameter 80 mm is inserted in a steel tube of inside diameter 80.2 mm and then compressed by axial force P. The gap between steel tube and polyethylene bar will close when compressive load P is approximately:

A copper tube with wall thickness of 8 mm must carry an axial tensile force of 175 kN. The allowable tensile stress is 90 MPa. The minimum required outer diameter is approximately: $\text { MPa. }$

circular aluminum tube of length L = 650 mm is loaded in compression by forces P. The outside and inside diameters are 80 mm and 68 mm, respectively. A strain gage on the outside of the bar records a normal Strain in the longitudinal direction of 400 $400 \times 10 ^ { - 6 }$ . The shortening of the bar is approximately:

An elastomeric bearing pad is subjected to a shear force V during a static loading test. The pad has dimensions a = 150 mm and b = 225 mm, and thickness t = 55 mm. The lateral displacement of the top plate with respect to the Bottom plate is 14 mm under a load P = 16 kN. The shear modulus of elasticity G of the elastomer is approximately: