A beam made of steel is shown in figure- At collapse- the value of P is k MP-L- The value of k- rounded off to two decimal place is

Redundancy, r = 5 3 = 2 No. of hinges for collapse = 2 + 1 = 3 (i) Span AB Hinges form at A, B and at mid span nbsp; From the principle of virtual work 2 ...

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Standard XII

Physics

Time Period Independent of Amplitude

A beam made o...

Question

A beam made of steel is shown in figure. At collapse, the value of P is $k \frac{M_{P}}{L}$ . The value of k, (rounded off to two decimal place) is ______

4

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Solution

The correct option is A 4
Redundancy, r = 5 - 3 = 2

No. of hinges for collapse = 2 + 1 = 3

(i) Span AB
Hinges form at A, B and at mid span
From the principle of virtual work

$2 M_{P} θ + 2 M_{P} (2 θ) + M_{P} θ = \frac{1}{2} \times \frac{L θ}{2} \times L \times (\frac{P}{L})$

$7 M_{P} θ = \frac{P L θ}{4} \Rightarrow P = \frac{28 M_{P}}{L}$

(ii) Span BC
$M_{P} θ + M_{P} (2 θ) = \frac{P L θ}{2} - \frac{P}{2} \frac{L θ}{2}$

$P = \frac{12 M_{P}}{L}$

(iii) Span CD

$M_{P} θ = \frac{P}{2} . \frac{L}{2} θ$

$P = \frac{4 M_{P}}{L}$

$∴$ Collapse load, min of
$(\frac{4 M_{P}}{L}, \frac{12 M_{P}}{L}, \frac{28 M_{P}}{L})$
$= \frac{4 M_{P}}{L}$

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A beam made of steel is shown in figure. At collapse, the value of P is kMPL. The value of k, (rounded off to two decimal place) is ______ 4

A beam made of steel is shown in figure. At collapse, the value of P is $k \frac{M_{P}}{L}$ . The value of k, (rounded off to two decimal place) is ______

4