GATE 2017 CE (CE1) – Question 49
A stepped linear-elastic bar carries an axial tensile load of 1 kN. Segment 1 has $A_1=100$ mm², $E_1=2\times10^5$ MPa and $L_1=400$ mm. Segment 2 has $A_2=60$ mm², $E_2=3\times10^5$ MPa and $L_2=900$ mm. Find strain energy in N mm, to one decimal place.
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Correct answer: 34.9 to 35.1
Explanation
The same axial force $P=1000$ N passes through both segments. For a uniform segment, $U_i=P^2L_i/(2A_iE_i)$. Therefore $U_1=1000^2(400)/[2(100)(200000)]=10$ N mm and $U_2=1000^2(900)/[2(60)(300000)]=25$ N mm. Total strain energy is $10+25=35.0$ N mm.