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Type 2: Problems on Stepped Cross-section

1. A copper bar shown in figure is subjected to a tensile load of 30 KN. Determine elongation of the bar if E=100GPa. Also find maximum stress induced.

2. A copper bar 900mm long and circular in section . It consists of 200mm long bar of 40 mm diameter,500 mm long bar of 15 mm diameter and 200mm long bar of 30mm diameter. If the bar is subjected to a tensile load of 60kN,Find the total extension of the bar.Take E=100GPa

(Ans:1.963 mm)

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3.A stepped bar ABCD consists of three parts AB,BC and CD such that Ab is 300mm long and 20mm diameter, BC is 400mm long and 30mm diameter and CD is 200 mm long and 40 mm diameter. It was observed that the stepped bar undergoes a deformation of 0.42mm when it was subjected to a compressive load of P N. Find the value of P if E=200 GPa.

(Ans:50 kN)

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4.A steel rod is subjected to axial load of 50 kN. Total length of rod is 4m. First 1m has diameter 32mm, second 1m has diameter 28mm and remaining part has diameter 25mm. If Young's modulus of material is 2 105 N/mm2 .Find elongation of the rod.

(Ans:1.73 mm)

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5.A circular bar of 500mm length has first 100mm of diameter 12mm,second 200mm has diameter 20mm and the last 200mm has diameter of 30mm. Determine the maximum axial pull which the bar is subjected if the maximum stress is limited to 100 N/mm2 .Find the total elongation of the bar.E= 2 105 N/mm2

(Ans: P=11309.3 N, elongation=0.102)

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6.A bar of uniform cross sectional area 100mm2 is subjected to forces as shown below. Calculate the change in the length of the bar.Young's modulus of material is 2 105 N/mm2 

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8.A steel bar of 20mm diameter is loaded as shown in figure. Determine the stresses in each part and the total elongation. Take E=210 GPa.