# Type 3: Problems on Bi-axial and Tri-axial stress system

1. In a biaxial stress system the stresses along x direction is 60 N/mm2 tensile and along y direction 40 N/mm2 compressive .Find the maximum strain. Take E = 200Gpa and poisons ratio =0.25

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2. A rectangular bar 500mm long and 100 mm by 50mm in cross-section is subjected to forces as shown below.

What is the change in the volume of the bar? take modulus of elasticity of 200GPa and poisson’s ratio as 0.25.

(Ans: dv= 137.5 mm3)

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4.A steel cube block of 50 mm side is subjected to a force of 6kN(tension), 8 kN(compression) and 4 kN(tension) along x, y and z direction respectively. Determine the change in volume of the block. Take E as 200 Gpa and m as 10/3.

{dv=0.2 m^3}

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5. A steel bar 1.2 m long,50mm wide and 40 mm thick is subjected to an axial pull of 150 kN in the direction of its length. Determine the change in volume of the bar. Take E=200 GPa,m=4

(Ans:450 mm3 )

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6.A steel cube block of 100 mm side is subjected to a stress of 50 N/mm2 (tensile) in x direction, a stress of 40 N/mm2 (compressive) in y direction, a stress of 30 N/mm2 (tensile) in z direction, calculate strain in each direction and dv. E=200 Gpa, and Poisson ratio =0.25

(Ans:dv=100 mm3 )

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7.In a tri-axial stress system the stresses  along the three directions are 100 N/mm2 (tensile) in x direction, 60 N/mm2 (tensile) in y direction, 30N/mm2 (comp) in z direction, calculate strain in each direction and change in volume take E=200Gpa and Poisson ratio as 0.25 take x=400,y=150,z=300

(ans dv= 5850 mm3 )

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8. A cube of 100 mm side is subjected to a tensile force of 200 kN on all faces (tensile). Find the strains in each direction. Also find the change in volume of the cube.Take E as 200 Gpa and m =4.

(ans dv=150mm3)