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ESE Civil 2014 Paper 1: Official Paper

Option 3 : \(\frac{{32{M_p}}}{{3L}}\)

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

__Given__**:**

Fixed beam with concentrated load L/4 from one end

__Calculation__**:**

Number of Plastic hinges = D_{s} + 1 = (4 - 2) + 1 = 3

i.e. at A, B and C

From geometry,

\(\Delta = \frac{L}{4}{\theta _A}\) and \({\theta _A} = 3{\theta _B}\)

According to virtual work principle,

External work done = Internal work Done

\(W\Delta = {M_P}{\theta _A} + {M_P}{\theta _A} + {M_P}{\theta _B} + {M_P}{\theta _B}\)

\(W\frac{L}{4}{\theta _A} = 2{M_P}{\theta _A} + \frac{{2{M_P}{\theta _A}}}{3}\)

\(\Rightarrow W = \frac{{32}}{3}\frac{{{M_P}}}{L}\)