2000 Final Exam

# B determine the reactions at a and b c draw the shear

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Unformatted text preview: Determine the reactions at A and B. (c) Draw the shear force and bending moment diagrams, labeling all critical values. P B C k A L L/2 Figure 4 Name: Signature: Student Number: Information Sheet for CIVL 230 Exam Stresses and Strains ε = δ / L; γ = δ s / h; σ = P / A; τ = V / As bg σ = Eε ; τ = Gγ ; G = E / 2 1 + ν Axial Bar PL ; displacement of a uniform bar under uniform load AE LN x δ= dx ; displacement of a non - unifom bar under non - uniform load N x 0 EA δ= z bg bg displacement due to non - uniform temperature change ∆T b x g δT = z U= 1 P2 L ; strain energy of a uniform bar 2 AE L 0 bg α ∆T x dx ; Torsional Bar T τ Gϕ == ; torsion formula for a uniform bar under uniform torque T Jr L γL = ϕr ; relation between shear strain γ and angle of twist ϕ πR 4 J= ; polar 2nd moment of area for a solid circular section of radius R 2 LT x ϕ= dx ; twist at the end of a non - uniform bar of length L under non - uniform torque T x 0 GJ z bg bg Beam Bending y ρ M σE = − = ; bending stress formula for a homogeneous beam I yρ ε = − yκ = − bh3 ; 2nd moment of area of a rectangular section beam about the z axis 12 M Ei y σi = − ; bending stress in material i for a composite beam å Ei Ii I= i dM ; shear - moment relation dx VQ f= ; shear flow with Q = y dA ; 1st moment of area about the z axis I A V= z d 2v M = ; differential equation for beam deflection v dx 2 EI Name: Signature: Student Number: Information Sheet for CIVL 230 Exam Beam Deflections...
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