Explanation Given information: The steel bar is subjected to the tensile load of 500 lb. Modulus of elasticity of the steel is E = 29 × 10 3 ksi . Poisson’s ratio is ν = 0.3 . Calculation: The cross section of the steel bar is a rectangular cross section of 2 in . × 0.5 in . Find the cross sectional area as shown below. A = b × t Here, b is the width of the cross section and t is the thickness of the cross section. Substitute 2 in. for b and 0.5 in. for t . A = 2 × 0.5 = 1 in . 2 Find the normal stress along x direction as shown below. σ x = P A Here, P is the tensile load and A is the cross sectional area. Substitute 500 lb for P and 1 in . 2 for A . σ x = 500 1 = 500 psi Apply the normal strain in x direction as shown below. ε x = 1 E ( σ x − ν ( σ y + σ z ) ) Here, E is the modulus of elasticity, σ x is the normal stress in x direction, ν is the Poisson’s ratio, σ y is the normal stress in y direction, and σ z is the normal stress in z direction. Substitute 500 psi for σ x , 0 for σ y , 29 × 10 3 ksi for E , 0.3 for ν and 0 for σ z . ε x = 1 29 × 10 3 ksi × 1 , 000 psi 1 ksi ( 500 psi − 0.3 ( 0 + 0 ) ) = 17.24 × 10 − 6 Apply the normal strain in y direction as shown below. ε y = 1 E ( σ y − ν ( σ x + σ z ) ) Substitute 500 psi for σ x , 0 for σ y , 29 × 10 3 ksi for E , 0

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When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 10.5, Problem 10.24P

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The principal strains ε1, ε2, and ε3 .

To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.

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The principal strains ε 1 , ε 2 , and ε 3 . To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.

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The principal strains ε1, ε2, and ε3 . To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.

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The principal strains ε1, ε2, and ε3 .

To sketch: The deformed element due to the equivalent in-plane strains within x-y plane.