The rigid block has a weight of 500kN and is to be supported by posts A and B ,

Question

The rigid block has a weight of 500kN and is to be supported by posts A and B, which are made of A-36 steel, and the post C, which is made of C83400 red brass.

If all the posts have the same original length before they are loaded, determine the average normal stress developed in each post when post C is heated so that its temperature is increased by 10?C. Each post has a cross-sectional area of 5600mm2 .
Express your answers to three significant figures. Enter your answers separated by a comma.

PLEASE NOT THE ANSWES ARE NOT A,B 31.68 or 30.3 MPa and C 25.915 or 28.5 MPa

Explanation / Answer

Given that

W = 500 KN

Length of the beams are same

A = 5600 mm2

Esteel = 200 GPa & Ered brass = 117 GPa

We know that

2Ps + PB = 500 KN -------> (1)

dlS = dlB

PS.LS/(AS.ES) = PBLB/(AB.EB)

PS = (500 - 2PS)(200/117)

= 854.7 - 3.418 PS

   Therefore PS = 193.45 KN

Sub in equ (1)

2 (193.45) + PB = 500

PB = 500 - 386.91

= 113.082 KN

Now calculate stress

stress in steel rod = PS/AS = 193.45*1000/(5600) = 34.5 N/mm2

Stress in brass rod = PB/AB + E.et

= 113.082*1000/5600 + 117*1000*18.7*10-6*10

= 20.193+ 21.879

= 42.072 N/mm2

stresses in A, B, C are 34.5, 34.5, 42.072 MPa

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