3 Normal Stress Using the proportional correlation of stress and strain max x x

# 3 normal stress using the proportional correlation of

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3.3 Normal Stress Using the proportional correlation of stress and strain: max x, x σ c y σ = (3.13) in (3.11): = 0 F x : 0 dA y c σ dA σ c y dA σ max max x = = = dA y : first moment of cross section (statical moment) about the neutral axis =0 neutral axis = centroidal axis = 0 M z : z 2 max x M dA y c σ dA σ y = = z 2 max M dA y c σ = dA y I 2 = : second moment of cross section (moment of inertia) Transformation of (3.14): z z max I c M σ = (3.13) in (3.15): z z x I y M σ = Introducing: c I S = elastic section modulus (3.15) becomes: z z max S M σ = since I y M ε E σ = = I E y M = ε recalling (3.12): ρ y ε = in (3.18): κ = = ρ I E M 1 (continued in chapter 7, deflection of beams) (3.13) (3.14) (3.15) (3.16) flexual stress (linear elastic) elastic flecture formulas (3.17) (3.18) (3.19) curvature of neutral axis EI = bending or flexual stiffness fig 3.22: stress distribution along section of beam c x y neutral axis - σ max + σ max M z 24