Problem 3. It is daytime (21°C) on the construction site, and a cylindrical, alu

Question

Problem 3. It is daytime (21°C) on the construction site, and a cylindrical, aluminum rod of length L = 30 m, needs to be placed in a truss that only has a clearance of L-29.99 m. The team plans to wait until nighttime for the temperature to drop for the rod to fit into the truss. If ? = 22.2 x 10-6 mm. K, what must the outside temperature be for the construction team to place the rod? (a)15°C b) 15°C (c) 6°C (d) 36°C Problem 4. A square, steel column, E 29,000 ksi with sides b4 inches, is to hold a compression force of 1000 kips. What is the maximum length the column can be (consider stability only, K-1.0). (a) 0.2 feet (b) 2.81 feet (c) 3.67 feet (d) 6.51 feet

Explanation / Answer

3) Initial length of rod= 30 m
required length of rod=29.99m
required reduction length = 29.99-30=0.01 m
linear coefficient of thermal expansion=22*10-6 /oC
let required reduction in temperature = T
0.01=30*22.2*10-6*T
T=15 oC
since the length has to reduce, the chnage in temperature has to be negative
outside temperature required = 21-15=6oC
correct option is (c)

4) let the required length be L inches
buckling capapcity = pi2*E*I/L2 = (pi2*29000*4*43/12)/L2
(pi2*29000*4*43/12)/L2 = 1000
L=78.14 in = 6.51 ft
correct option is (d)

thankyou

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