# Type 2. Problems on Poissons ratio.

1. A metal rod 20 mm diameter and 2 m long is subjected to a tensile force of 60 kN, it showed and elongation of 2 mm and reduction of diameter by 0.006 mm. Calculate the Poisson's ratio and three moduli of elasticity.

(Ans:Poisson’s ratio = 0.3,E=190.99e3 N/mm2 ,G=73.45e3 N/mm2 ,K=159.15e3 N/mm2 )

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2. A bar of diameter 12 mm is tested on U.T.M and following observations were noted 1)Gauge length : 200mm 2) Load on Proportional limit :20kN 3)Change in length : 0.2 mm 4) Change in dia : 0.0025 mm. Determine E,G,K and u.

(Ans:Poisson’s ratio = 0.208,E=176.85e3 N/mm2,G=73.19e3 N/mm2,K=100.94e3 N/mm2 )

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3. A metal bar 50mm50mm in section is subjected to an axial compressive load of 500 kN. If the contraction of a 200mm gauge length was found to be 0.5 mm and the increase in thickness 0.04 mm, find Poisson’s ratio and three moduli.

(Ans:E=80Gpa, Poisson's ratio=0.32)

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4.In an experiment an alloy bar of 1m long and 20mm20mm in section was tested to increase through 0.1 mm, when subjected to an axial tensile load of 6.4 kN. If the value of bulk modulus of the bar is 133 GPa, find the value of Poisson's ratio

(Ans: Poisson's ratio=0.30)

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5. A steel rod 4 m long and 20mm diameter is subjected to an axial tensile load of 45 kN. Find the change in length and diameter of the rod. E= 200 GPa, and m=4.

(Ans: Change in length=2.86mm, change in diameter =0.003575mm)

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6.A steel rod 3m long and 25mm diameter is subjected to an axial tensile load of 60 kN. Calculate the change in length and diameter of rod. E=210 Gpa and u=0.28.

(Ans: Change in length=1.75mm, change in diameter =0.0041mm)

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7.A steel bar 1.2 m long, 40mm wide and 20 mm thick is subjected to an axial tensile load of 50 kN in the direction of its length. Find the change in length and thickness of the bar . E=200 Gpa and Poisson's ratio =0.26.

(Ans: Change in length=0.375mm, change in thickness=1.62510-3mm)

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8.A metal bar 40mm40mm section, is subjected to an axial compressive load of 480 kN. The contraction of a 200 mm gauge length is found to be 0.4 mm and the increase in thickness 0.04 mm. Find Young’s Modulus and Poisson’s ratio.

(Ans: E= 150103 n/mm2 , m=2)

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9. For a metal bar of 20 mm diameter and 1m long is subjected to an axial pull of 60 KN Take and .Find the change in the diameter of the bar.