Question

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

Answer 1

7.48 Kip

Step-by-step explanation:

Properties of steel

Young’s modulus is 29000 Ksi

`\alpha=6.5*10^(-6)`

Point load for simply supported beam is given by

`V_c=\frac {pl^(3)}{48EI}` 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

`V_c=\frac {F_(CD)*120^(3)}{48*29000*475}=0.002613F_(CD)`

The change in length due to axial load is given by

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

Deflection due to temperature stress is given by

`\delta_T=\alpha \triangle TL=6.5*10^(-6)*150*50` where L is the length of the rod, taken as 50 inches

`\delta_T=0.04875 in`

`0.002613F_(CD)=0.04875+(-0.003903F)`

`F_(CD)=7.48 kip`