Derive the equation for the elastic deflection curve

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Reference no: EM132365828

Problems -

1. For the beam shown below, derive the equation for the elastic deflection curve, y(x), using Bernoulli-Euler Beam Theory. What is the equation for the deflection at mid-span?

2. For the beam shown below, derive the equation for the elastic deflection curve, y(x), using Timoshenko Beam Theory. What is the equation for the deflection at mid-span?

Plot the ratio of mid-span deflection from Problem 1 to Problem 2 for L = 25 to 300 inches. For this, use E = 29000 ksi, I = 1350 in⁴, G = 11200 ksi. A_s = 9.322 in². What can be concluded about the effect of shear deformations on the behavior of a beam?

3. For the beam-column shown below, derive the equation for the elastic deflection curve using Bernoulli-Euler Beam Theory. What is the equation for the maximum deflection at mid-span?

Comparing the equations for mid-span deflection in Problems 1 and 3, what can be concluded about the effect of an axial compression force on the behavior of a beam-column? [Hint: simplify the final equation by using u = λL/2].

Reference no: EM132365828

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