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# Shear Force and Bending Moment Civil Engineering (CE) Notes | EduRev

## Civil Engineering (CE) : Shear Force and Bending Moment Civil Engineering (CE) Notes | EduRev

The document Shear Force and Bending Moment Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
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Shear Force and Bending Moment

SHEAR FORCE AND BENDING MOMENT
1. SHEAR FORCE at the cross- section of a beam may be defined as the unbalanced vertical force to the right or  left of the section.

2. BENDING MOMENT at the cross- section of a beam may be defined as the algebraic sum of the moment of the forces, to the right or left of the section.

3. BEAM is a structural number subjected to transverse loads only.

4. BEAMS can be classified as :
(i) Cantilever
(ii) Simply supported
(iii) Overhanging
(iv) Rigidly fixed OR Built- in
(v) Continuous

5. Shear force and bending moment diagrams: Sign Convention:

(i) Shear force

(ii) Bending moment

SFD and BMD for cantilever beams: (i) Cantilever of length l carrying a concentrated load W at the free end
S= + W

M= – Wx

Mmax = – WL

(ii) Cantilever of length l carrying a uniformly distributed load of 'w' per unit run over the  whole length
Sx = + wx

Smax = + wl

(iii) Cantilever of length l carrying a uniformly distributed load of 'w' per unit run over the whole length and a concentrated load W at the free end Sx = wx + W

Smax = wl + W

(iv) Cantilever of length l carrying a uniformly distributed load of 'w' per unit run for a distance 'a' form free end form D to B,

Sx = + wx

form A Sx = + wa

(v) Cantilever of length 'l' carrying a load whose intensity varies uniformly from zero at free end to 'w' per unit run at the fixed end

= area of load diagram between X and B,

Mx = Moment of load acting on XB about X = area of the load diagram between X and B × distance of centroid of this diagram form X

(vi) Cantilever carrying a load whose  intensity varies uniformly form zero at the fixed end to w per unit run at the free  end

SFD and  BMD for simply supported beams: (i) Simply supported beam of span l carrying a concentrated load at mid span

Sx = +  (between AC)
Sx = –   (between CB)
Mx = +  x (between CB)
Mx = + x (form A to C) (at a distance 'X' form A)
Mmax = Mc =

(ii) Simply supported beam carrying a concentrated load placed eccentrically on the span

Sx  =  +  (form A to D)
= – (form D to B)
Mx = +  x (form A to D) at a distance 'x' form  A
Mmax = MD =

NOTE: Maximum B.M. occurs where S.F. changes its sign.

(iii) Simply supported beam carrying a uniformly distributed load of w per unit run over the whole span

(iv) Simply supported beam carrying a load whose intensity varies uniformly from zero at each end to 'w' per unit run at the mid span

(v) Simply supported  beam carrying a load whose intensity varies uniformly from zero at one end to 'w' per unit run at the other end

Mmax B.M. occurs at x =   form end A
Mmax

SFD and BMD for simply supported beams with overhang: Simply supported beam with equal overhangs and carrying a uniformly distributed load of 'w' per unit run over the whole length S.F. at any section in EA at a distance x form E,
Sx = –wx at any section in A.B,

Sx = (w/2)(l + 2a )– wx

B.M. at any section in EA,

at any section in AB.

at x = 'a' and 'a + l' i.e., at A & B,

Mc = (w/2)( l2 - 4a2 )

Case (a) :

∴  B.M.D. will be as shown in figure above of contraflexure O1 & O2 are at a distance

form   centre.
Thus  distance between point of contraflexure OO=

Thus  distance between point of contraflexure

Case (b) :

B.M at C = Mc = 0 The beam will be subject to only  hogging moments.
Points of contraflexure O1 & O2 will coincide with C.
B.M.D will be as shown in figure (a)

Mc is negative ,since l2 < 4a2

B. M.  will be zero only at ends A and D and at all other sections B.M. will be of hogging type B.M. and S.F due to a couple

Case (a): Cantilever There will be no shear force

Case (b): Simple supported
Shear force is constant

B.M., Mx = –  (left of C)
= + (right of C)

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## Civil Engineering SSC JE (Technical)

109 docs|50 tests

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