Exam 10: Stresses in Beams

A cast iron pipe $\left( L = 12 \mathrm {~m} \text {, weight density } = 72 \mathrm { kN } / \mathrm { m } ^ { 3 } , d _ { 2 } = 100 \mathrm {~mm} \text {, and } d _ { 1 } = 75 \mathrm {~mm} \right)$ is lifted by a hoist. The lift points are 6 m apart. The maximum bending stress in the pipe is approximately:

$\text { A composite beam is made up of a } 200 \mathrm {~mm} \times 300 \mathrm {~mm} \text { core } \left( E _ { c } = 14 \mathrm { GPa } \right) \text { and an exterior cover sheet }$ $\left( 300 \mathrm {~mm} \times 12 \mathrm {~mm} , E _ { e } = 100 \mathrm { GPa } \right)$ on each side. Allowable stresses in core and exterior sheets are $9.5 \mathrm { MPa }$ and $140 \mathrm { MPa }$ , respectively. The ratio of the maximum permissible bending moment about the $z$ axis to that about the $y$ axis is most nearly:

Two thin cables, each having a diameter of d = t/6 and carrying tensile loads P, are bolted to the top of a rectangular steel block with cross-sectional dimensions $b \times l$ . The ratio of the maximum tensile to compressive Stress in the block due to loads P is:

A simply supported wood beam (L = 5 m) with rectangular cross section (b = 200 mm, h = 280 mm) car- ries uniform load q = 6.5 kN/m includes the weight of the beam. The maximum flexural stress is approximately:

A beam with an overhang is loaded by a uniform load of 3 kN/m over its entire length. Moment of iner- tia $I _ { z } = 3.36 \times 10 ^ { 6 } \mathrm {~mm} ^ { 4 }$ and distances to top and bottom of the beam cross section are 20 mm and 66.4 mm,Respectively. It is known that reactions at A and B are 4.5 kN and 13.5 kN, respectively. The maximum bending Stress in the beam is approximately:

A simply supported steel beam of length L = 1.5 m and rectangular cross section ( $( h = 75 \mathrm {~mm} , b = 20 \mathrm {~mm} )$ carries a uniform load of $q = 48 \mathrm { kN } / \mathrm { m } \text { that includes its own weight. }$ 48 kN/m that includes its own weight. The maximum transverse shear stress on the cross section at 0.25 m from the left support is approximately:

A simply supported laminated beam of length L = 0.5 m and square cross section weighs 4.8 N. Three strips are glued together to form the beam, with the allowable shear stress in the glued joint equal to 0.3 MPa. Considering also the weight of the beam, the maximum load P that can be applied at $L / 3$ from the left support Is approximately:

An aluminum light pole weighs 4300 N and supports an arm of weight 700 N, with the arm center of gravity at 1.2 m left of the centroidal axis of the pole. A wind force of 1500 N acts to the right at 7.5 m above The base. The pole cross section at the base has an outside diameter of 235 mm and thickness of 20 mm. The Maximum compressive stress at the base is approximately:

$\text { A composite beam of aluminum } \left( E _ { a } = 72 \mathrm { GPa } \right) \text { and steel } \left( E _ { s } = 190 \mathrm { GPa } \right) \text { has a width } b = 25 \mathrm {~mm} \text { and }$ $\text { heights } h _ { a } = 42 \mathrm {~mm} \text { and } h _ { s } = 68 \mathrm {~mm} \text {, }$ , respectively. A bending moment is applied about the z axis resulting in a maximum stress in the aluminum of 55 MPa. The maximum stress in the steel is approximately: $\text { MPa. }$

A rectangular beam with semicircular notches has dimen sions $h = 160 \mathrm {~mm} \text { and } h _ { 1 } = 140 \mathrm {~mm}$ maximum allowable bending stress in the plastic beam is $\sigma _ { \max } = 6.5 \mathrm { MPa }$

A bimetallic beam of aluminum $\left( E _ { a } = 70 \mathrm { GPa } \right) \text { and copper } \left( E _ { c } = 110 \mathrm { GPa } \right)$ strips has a width of b = 25 mm; each strip has a thickness of t = 1.5 mm. A bending moment of 1.75 N . m is applied about The z axis. The ratio of the maximum stress in aluminum to that in copper is approximately:

A copper wire (d = 1.5 mm) is bent around a tube of radius R = 0.6 m. The maximum normal strain in the wire is approximately:

A cantilever wood pole carries force P = 300 N applied at its free end, as well as its own weight (weight density = $\left. 6 \mathrm { kN } / \mathrm { m } ^ { 3 } \right)$ ). The length of the pole is L = 0.75 m and the allowable bending stress is 14 MPa. the required diameter of the pole is approximately:

A steel hanger with solid cross section has horizontal force P = 5.5 kN applied at free end D. Dimension variable b = 175 mm and allowable normal stress is 150 MPa. Neglect self-weight of the hanger. The required Diameter of the hanger is approximately:

An aluminum cantilever beam of length L = 0.65 m carries a distributed load, which includes its own weight, of intensity $q / 2 \text { at } A \text { and } q \text { at } B \text {. }$ . The beam cross section has a width of 50 mm and a height of 170 mm.Allowable bending stress is 95 MPa and allowable shear stress $12 \mathrm { MPa }$ The permissible value of load inten-Sity $q$ is approximately: