MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Newton's Second Law: Rotatory Version

A prismatic, ...

Question

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L,Young's modulus E and area moment of inertia I, the magnitude of the maximum deflection is

A

\frac{q L^{4}}{10 E I}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{q L^{4}}{60 E I}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{q L^{4}}{15 E I}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{q L^{4}}{30 E I}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{q L^{4}}{30 E I}$

By using moment area IInd theorem
$Y_{B} - Y_{A}$ $= A ¯ ¯¯¯ ¯ X o f \frac{M}{E I}$ diagram between B and A
$Y_{m a x} - 0 = (\frac{1}{4}) (\frac{q L^{2}}{6 E I}) (L) (\frac{4 L}{5})$
$Y_{m a x} = \frac{q L^{4}}{30 E I} (↓)$

Suggest Corrections

thumbs-up

1

Similar questions

Q. A cantilever beam of length

L

is subjected to a moment

M

at the free end. The moment of inertia of the beam cross section about the neutral axis is

I

and the young's modulus is

E

. The magnitude of the maximum deflection is

Q. A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment ,M, as shown in the figure. The deflection of the beam at

x = \frac{L}{2}

Q. A cantilever beam of length

l

, and flexural rigidity

E I

,stiffened by a spring of stiffness k, is loaded by transverse force

P

The transverse deflection under the load is

Q. A cantilever beam of

l

subjected to a uniformly distributed load

^{'} w^{'}

per unit length resting on a rigid prop at the tip of cantilever. The magnitude of the reaction at the prop is:

Q. A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2 kN normal to the top surface as shown in the figure. The Young's modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope (in radian) at Q (20 mm from the fixed end) is _________ .

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Old Wine in a New Bottle

PHYSICS

Watch in App

explore_more_icon

Explore more

Newton's Second Law: Rotatory Version

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon