Subject: Structural Analysis II

Topic: Flexibility Method

Difficulty: Medium / High

1) Free Bending moment: [considering each span simply supported]

• For Span AB B mat $E=\frac{wab}{l}$ =$\frac{80(2)(4)}{6}=\underline{106.6 kN.m}$
• For Span BC B mat $f=\frac{wl^{2}}{8}$=$\frac{20(5)^{2}}{8}=\underline{62.5 kN.m}$
• For Span CD B mat $G=\frac{wab}{l}$=$\frac{60(2)(3)}{5}=\underline{72kN.m}$

2) Free Bending moment diagram

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3) Three moment Theorem

• For A-B-C $m_{A}(l_{1})+2m_{B}(l_{1}+l_{2})+m_{c}(l_{2})+\frac{6A_{1}x_{1}}{l_{1}}+\frac{6A_{2}x_{2}}{l_{2}}=0$ $0+2MB(6+5)+M_{c}(5)+\frac{6 \times (320.01)(2.67)}{6}+\frac{6(208.33)(2.5)}{5}=0$ $22M_{B}+5M_{c}=-1479.42 \tag{1}$

  -For A-B-C …