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Calculate the vertical & horizontal displacements at point C in the simple frame with uniform flexural rigidity as shown in fig. Use unit load method. Also draw the deflected profile of the frame.
written 6.3 years ago by gravatar for teamques10 teamques10 ★ 65k •   modified 2.3 years ago

Subject: Structural Analysis 1

Topic: Deflection of Beams using Energy Method

Difficulty: High

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structural analysis
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written 6.3 years ago by gravatar for teamques10 teamques10 ★ 65k •   modified 6.1 years ago

1. Reaction

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2. For horizontal deflection at C

enter image description here

3. For vertical deflection at C

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Region origin limits Mu Mu Hor. Mu Vert.
AB A 0-4 $$8x-\frac{2x^2}{2}-20$$ $x-4$ $-2$
BC C 0-2 $-2x$ $-x$ $-x$

$\begin{align} &\Delta H_C= \int_0^4 (8x-x^2-20)(x-4)\frac{dx}{EI}+\int_0^2 (-2x)(0)\frac{dx}{EI} \\&\phantom{\Delta H_C}=\frac{1}{EI} \int_0^4 \left[8x^2-32x-x^3+4x^2-20x+80\right]dx \\&\phantom{\Delta H_C}=\frac{1}{EI} \int_0^4 \left[-x^3+12x^2-\frac{52x^2}{2}+80\right]dx \\& \Delta …

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