GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 18 of 65

Marks: +1, -0

A planar elastic structure is subjected to uniformly distributed load, as shown in the figure(not drawn to the scale)

Neglecting self-weight, the maximum bending moment generated in the structure (in kN.m,round off to the nearest integer), is ____________.

Solution:

Σ {F}_{ {x}}=0 ⇒ {H}_{ {A}}=0

Neglecting self weight, the maximum bending moment. Taking "A" as the origin and springing points '

A^{' '}

and '

B^{' '}

are at the same level.
Applying,

Σ {MA}=0

to the

{FBD}

of entire arch.

⇒ 12 × 8 ×(\;{8}/{ {L}})- {v}_{ {B}}[8]=0

⇒ {VB}=48 {KN}

{M}_{ {x}}+12 {x}(\;{ {x}}/{2})- {V}_{ {B}}[ {x}]=0

{M}_{ {x}}= {V}_{ {B}}[ {X}]-6[ {x}^{2}]

⇒ {M}_{ {x}}=48( {x})-6( {x}^{2})

For max B.M

\;{d M_{x}}/{d x}=0

⇒ 48-12 × 20 ⇒ x=4 m

(M x) \max =48(4)-6(4)^{2}=96 {KN}- {m}

Go to Question:

Prev Question

Next Question