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ENGR 225 Section 2.1
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Review ~ Force per Area Normal Stress –The average normal stress can be determined from σ = P / A, where P is the internal axial load. Shear Stress –The average shear stress can be determined from τ = V / A, where V is the resultant shear force.
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Strain Deformation due to a stress is specified using the concept of normal and shear strain.
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Normal Strain Elongation or contraction of a line segment per unit of length.
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Shear Strain The change in angle the occurs between two line segments that were originally perpendicular.
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Volume and shape deformations
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Strain Normal strain causes a change in volume Shear strain causes a change in shape
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Positive and Negative strain Normal strain : Initial line elongates : L positive, strain positive Initial line contracts : L negative, strain negative Shear strain : ’ < /2 : Strain positive ’ > /2 : Strain negative
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Small strain Analysis Deformations very small Normal strain < < 1 sin ≈ tan ≈ cos ≈ 1
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Problem 2-4: Find the normal strain developed in each wire if the force P cause point A to be displaced 2mm horizontally.
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2.8 Part of a control linkage for an airplane consists of a rigid member CBD and a flexible cable AB. If a force applied to the end D causes CBD to rotate by 0.3 , determine the normal strain in the cable. Originally the cable is un-stretched.
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