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ENGR 225 Section 2.1

ENGR 225 Section 2.1. 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. Strain.

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ENGR 225 Section 2.1

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  1. ENGR 225Section 2.1

  2. 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.

  3. Strain • Deformation due to a stress is specified using the concept of normal and shear strain.

  4. Normal Strain • Elongation or contraction of a line segment per unit of length.

  5. Shear Strain • The change in angle the occurs between two line segments that were originally perpendicular.

  6. Volume and shape deformations

  7. Strain • Normal strain causes a change in volume • Shear strain causes a change in shape

  8. 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

  9. Small strain Analysis Deformations very small Normal strain  < < 1 sin ≈  tan ≈  cos ≈ 1

  10. Problem 2-4: Find the normal strain developed in each wire if the force P cause point A to be displaced 2mm horizontally.

  11. 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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