Total Longitudinal Strain Of A Rectangular Steel Block Under Combined Stress
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Total Longitudinal Strain Of A Rectangular Steel Block Under Combined Stress

The dimensions of a rectangular steel block are:
Length = 12 in, height = 4 in, thickness = 2 in.
Member is subjected to the following stresses:
Longitudinal tensile stress σx = 12,000 lb/in2
Vertical compressive stress σy = 15,000 lb/in2
Lateral compressive stress σx = 9,000 lb/in2
Poisson ratio μ, = 0.30.
Modulus of Elasticity of Steel E, = 30, 000,000.

Determine total longitudinal strain (i.e, total change in length).

The strings: S7P5A51 (Physical Change).

The math:
Pj Problem of Interest is of type change (Physical Change).

Assumptions: Principles of consistent deformation and superposition are applicable. Elasticity holds.
Combined stress are generally of two types:
(1) Combination of tensile and commpressive stresses (usually referred to as biaxial or triaxial stress).
(2) Combination of tensie, compressive and shear stresses (usually referred to as combined stress).

Equations of Interest:
Poisson ratio μ = (lateral unit strain)/(longitudinal unit strain)--------(1)
Strain = stress/Modulus of Elasticity = σ/E---------(2)
Total longitudinal strain = (length of member)x(sum of unit strains due to individual stresses)

(a) So, Total longitudinal strain = 12[12000/(30x106) + 0.30(1500)/(30x106) + 0.30(9000)/(30x106)]
= 12(+ 0.000400 + 0.000150 + 0.000090) = 12(0.00064) = 0.00768 in.

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