Exam 8: Axially Loaded Members

A steel plane truss is loaded at B and C by forces P =200 kN. The cross-sectional area of each member $\text { is } A = 3970 \mathrm {~mm} ^ { 2 }$ . Truss dimensions are H=3 m and L = 4 m. The maximum shear stress in bar AB is approx- imately:

$\text { A threaded steel rod } \left( E _ { s } = 210 \mathrm { GPa } , d _ { r } = 15 \mathrm {~mm} \text {, cte } e _ { s } = 12 \times 10 ^ { - 6 / { } ^ { \circ } \mathrm { C } } \right) \text { is held stress-free between rigid }$ walls by a nut and washer $\left( d _ { w } = 22 \mathrm {~mm} \right)$ assembly at each end. If the allowable bearing stress between the washer and wall is $55 \mathrm { MPa }$ and the allowable normal stress in the rod is $90 \mathrm { MPa }$ , the maximum permissible temperature drop $\Delta T$ is approximately:

A steel bar of rectangular cross section (a = 38 mm, b = 50 mm) carries a tensile load P. The allowable stresses in tension and shear are 100 MPa and 48 MPa, respectively. The maximum permissible load $P _ { \max }$ is Approximately:

A copper bar (d = 10 mm, E = 110 GPa) is loaded by tensile load P = 11.5 kN. The maximum shear stress in the bar is approximately:

nylon bar (E = 2.1 GPa) with diameter 12 mm, length 4.5 m, and weight 5.6 N hangs vertically under its own weight. The elongation of the bar at its free end is approximately:

brass bar (E = 110 MPa) of length $L = 2.5 \mathrm {~m} \text { has diameter } d _ { 1 } = 18$ mm over one-half of its length and $\text { diameter } d _ { 2 } = 18$ mm over the other half. Compare this nonprismatic bar to a prismatic bar of the same volume of material with constant diameter d and length L. The elongation of the prismatic bar under the same load P = 25 kN is approximately:

wires, one copper and the other steel, of equal length stretch the same amount under an applied load P. The moduli of elasticity for each is $E _ { s } = 210 \mathrm { GPa } \text { and } E _ { c } = 120 \mathrm { GPa } .$ GPa. The ratio of the diameter of the copper Wire to that of the steel wire is approximately:

A steel bolt $\left( \text { area } = 130 \mathrm {~mm} ^ { 2 } , E _ { s } = 210 \mathrm { GPa } \right)$ is enclosed by a copper tube (length = 0.5 m, area = $\left. 400 \mathrm {~mm} ^ { 2 } , E _ { c } = 110 \mathrm { GPa } \right)$ and the end nut is turned until it is just snug. The pitch of the bolt threads is 1.25 mm. The bolt is now tightened by a quarter turn of the nut. The resulting stress in the bolt is approximately:

$\text { A steel rod } \left( E _ { s } = 210 \mathrm { GPa } , d _ { r } = 12 \mathrm {~mm} , \text { cte } _ { s } = 12 \times 10 ^ { - 6 } / { } ^ { \circ } \mathrm { C } \right) \text { is held stress-free between rigid walls by a }$ clevis and pin $\left( d _ { p } = 15 \mathrm {~mm} \right)$ assembly at each end. If the allowable shear stress in the pin is $45 \mathrm { MPa }$ and the allowable normal stress in the rod is $70 \mathrm { MPa }$ , the maximum permissible temperature drop $\Delta T$ is approximately:

$\text { A monel shell } \left( E _ { m } = 170 \mathrm { GPa } , d _ { 3 } = 12 \mathrm {~mm} , d _ { 2 } = 8 \mathrm {~mm} \right) \text { encloses a brass core } \left( E _ { b } = 96 \mathrm { GPa } , d _ { 1 } = 6 \mathrm {~mm} \right)$ Initially, both shell and core have a length of 100 mm. A load P is applied to both shell and core through a cap plate. The load P required to compress both shell and core by 0.10 mm is approximately:

$\text { A brass rod } ( E =110 \mathrm { GPa } ) \text { with a cross-sectional area of } 250 \mathrm {~mm} ^ { 2 } \text { is loaded by forces } P _ { 1 } = 15 \mathrm { kN }$ $P _ { 2 } = 10 \mathrm { kN }$ , and $P _ { 3 } = 8 \mathrm { kN }$ . Segment lengths of the bar are $a = 2.0 \mathrm {~m} , b = 0.75 \mathrm {~m}$ , and $c = 1.2 \mathrm {~m}$ . The change in length of the bar is approximately:

plane truss with span length L = 4.5 m is constructed using cast iron pipes $( E = 170 \mathrm { GPa } )$ with a cross-sectional area of $4500 \mathrm {~mm} ^ { 2 }$ The displacement of joint B cannot exceed 2.7 mm. The maximum value of Loads P is approximately:

nonprismatic cantilever bar has an internal cylindrical hole of diameter $d / 2$ from 0 to x, so the net area of the cross section for Segment 1 $\text { is } ( 3 / 4 ) A \text {. Load } P \text { is applied at } x \text {. }$ $\text { and load } - P / 2$ is applied at x 5 L. Assume That E is constant. The length of the hollow segment, x, required to obtain axial displacement δ 5 PL/EA at the Free end is:

A brass wire (d = 2.0 mm, E = 110 GPa) is pretensioned to T = 85 N. The coefficient of thermal expan- sion for the wire is $19.5 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . The temperature change at which the wire goes slack is approximately:

A plane stress element on a bar in uniaxial stress has a tensile stress of $\sigma _ { \theta } = 78 \mathrm { MPa }$ (see figure). The maximum shear stress in the bar is approximately:

A prismatic bar (diameter $\text { (diameter } d _ { 0 } = 18 \mathrm {~mm} \text { ) is loaded by force } P _ { 1 } \text {. A stepped bar (diameters } d _ { 1 } = 20 \mathrm {~mm} \text { and }$ $d _ { 2 } = 25 \mathrm {~mm}$ with radius of fillets $R = 2 \mathrm {~mm}$ ) is loaded by force $P _ { 2 }$ . The allowable axial stress in the material is $75 \mathrm { MPa }$ . The ratio $P _ { 1 } / P _ { 2 }$ of the maximum permissible loads that can be applied to the bars, considering stress concentration effects in the stepped bar, is: