05-Material Property Relationships

05-Material Property Relationships - Material-Property...

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Material-Property Relationships Civ E 270 Khattak, N 1 Shear Stress-Strain OR 2 xy γ Shear Strain ° xy measures the angular distortion of the element relative to the sides shown originally along the x and y axes. The shear stress-strain relationship is established by testing thin circular tubes, subjected to torsional loading. By measuring the applied torque and the resulting angle of twist, a shear stress-strain diagram is plotted. Hooke’s Law for Shear γ τ G = Where; G = Shear Modulus of elasticity or the modulus of rigidity Units of G = rad MPa = MPa 2 xy γ ± xy ± xy x y = ± ° ° failure ° pl. ° u ° ± Proportional Limit G 1 Linear Elastic Behaviour
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Material-Property Relationships Civ E 270 Khattak, N 2 Example 5.1 Determine the vertical displacement at D, due to the shear strain in the rubber, if a force of 10 N pulls down at D. Area of cross section of rubber pads = 20 mm x 20 mm G r = 0.20 MPa D A B C 50 mm 50 mm 10 N Rubber pads Rigid plates
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Material-Property Relationships Civ E 270 Khattak, N 3 Example 5.2 Determine the horizontal deflection at the top if a force of 50 kN pulls the rigid plate to the right. Assume the rigid plate to be bonded perfectly to the supporting block. G = 400 MPa P = 50 kN Rigid 150 mm 90 mm 60 mm
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Material-Property Relationships Civ E 270 Khattak, N 4 L y L x ² x 2 ² x 2 ² y 2 ² y 2 P Poissons Ratio When a body is subjected to an axial force, not only it elongates but also contracts laterally. Longitudinal Strain; x x x L Δ = ε Lateral Strain; y y y L Δ - = ε , z z z L Δ - = ε Poisson’s Ratio al longitudin lateral ε ε ν - = = x y ε ε - Poisson’s Ratio is dimensionless. We take the absolute value if considering the ratio. Will keep the sign if showing the strain. For an isotropic and homogeneous material, a unique Poisson’s ratio exists in the elastic region.
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