The beam AB has a moment of inertia I= 475 in 4 and rests on the smooth supports at its ends. A 0.75-in.-diameter rod CD is welded to the center of the beam and to the fixed support at D. If the temperature of the rod is decreased by 150°F, determine the force developed in the rod. The beam and rod are both made of A-36 steel

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opudodennis opudodennis · Answer 1 · 2019-11-08T13:23:18+01:00

Answer:

7.48 Kip

Explanation:

Properties of steel

Young’s modulus is 29000 Ksi

[tex]\alpha=6.5*10^{-6}[/tex]

Point load for simply supported beam is given by

[tex]V_c=\frac {pl^{3}}{48EI}[/tex] where P is the point load, l is the length, I is moment of inertia

Taking length as 10 ft hence converted to inches we have 10*12=120 in

[tex]V_c=\frac {F_{CD}*120^{3}}{48*29000*475}=0.002613F_{CD}[/tex]

The change in length due to axial load is given by

[tex]\delta_f=\frac {PL}{AE}=\frac {F_{CD}*50}{0.25\pi (0.75)^{2}*29000}=0.003903F_{CD}[/tex]

Deflection due to temperature stress is given by

[tex]\delta_T=\alpha \triangle TL=6.5*10^{-6}*150*50[/tex] where L is the length of the rod, taken as 50 inches

[tex]\delta_T=0.04875 in[/tex]

[tex]0.002613F_{CD}=0.04875+(-0.003903F)[/tex]

[tex]F_{CD}=7.48 kip[/tex]