A fixed beam of variable cross section is shown in figure. If the value of collapse load is $\frac{k M_{P}}{L}$ then , the value of k will be ______

Open in App

Solution

Case I :

$L (θ) = 2 L (α)$
$\Rightarrow θ = 2 α$
$2 M_{P} (θ) + 2 M_{P} (θ + α) + 4 M_{P} α = P . L . θ$
$\Rightarrow 4 M_{P} θ + 3 M_{P} θ = P . L . θ$
$\Rightarrow P = \frac{7 M_{P}}{L}$

Case II :

$(2 L) θ = α L$
$\Rightarrow α = 2 θ$
$2 M_{P} (θ) + 2 M_{P} (θ + α) + + 4 M_{P} (α) = P L θ$
$\Rightarrow P = \frac{16 M_{P}}{L}$

Case III:

$2 M_{P} (θ) + 2 M_{P} (θ + θ) + 2 M_{P} (θ) = P L θ$
$\Rightarrow P = \frac{8 M_{P}}{L}$

So,
$P = \frac{7 M_{P}}{L} = \frac{k M_{P}}{L}$
$\Rightarrow k = 7$

Suggest Corrections

Similar questions

M_{p}

k \frac{M_{p}}{L}

A propped cantilever ABCD is loaded as shown in

figure. If it is of uniform cross- section, the collapse

load of the beam is k \frac{M_{p}}{L}, The value of k will be_____.

k \frac{M_{P}}{L}

α \frac{M_{p}}{L}

α

Join BYJU'S Learning Program