Stress_Analysis_Equations

Stress_Analysis_Equations - 1 Chapters 2 Materials Tensile...

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1 5/13/2009 Chapters 2: Materials Tensile and compressive stress (p. 28): 0 A / F = σ o (compresion = “-”, tension= “+”) Strain (p. 29): 0 0 / ) ( - = ε Hooke’s Law (p. 29): ε = σ E o E = modulus of elasticity = slope of linear region o S y (= σ y ) = yield strength o S u (= σ u ) = ultimate strength (or tensile strength) Chapter 3: Load and Stress Analysis Shear force (V) and bending moments (M)in beams (p. 71) o To find V at given x, break beam and set Σ F y =0 o To find M at given x, break beam and set Σ M =0 o Shear force = = = Vdx M ; dx dM V o Load intensity = = = = qdx V ; dx M d dx dV q 2 2 o For distributed forces (w=force/meter), replace with F = w x at center of region for calculating shear and moment o For non-uniform distributed forces replace with = dx ) x ( f F located at centroid (1/3 point for triangle) Singularity Functions (p. 73) o Concentrated moment at x=a: q = M 1 <x-a> -2 (M 1 = “+” for CW, “-” for CCW) o Concentrated force at x=a: q = F 1 <x-a> -1 (F 1 = “+” for upward, “-” for downward) o Distributed force starting at x=a & ending at x=b: q = W 1 <x-a> 0 - W 1 <x-b> 0 (W 1 = “+” for upward, “-” for downward) o Ramp force starting at x=a: q = R 1 <x-a> 1 o 1 2 a x dx a x - - - < = - < ; 0 1 a x dx a x - < = - < - o 1 0 a x dx a x - < = - < ; 2 1 a x 2 1 dx a x - < = - < o To find V and M functions Define q from the various component forces and moments
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