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Shear Force and Bending Moment

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Beam:
Beam is structural horizontal member which transfer external load including its own weight.
Type of beams:
1. Simply supported beam - A beam which both end are freely supported at its end on walls or columns are called simply supported beam.
2. Cantilever beam - A beam is fixed at one end and free at other end are called cantilever beam.

3. Overhanging beam - If end portion of beam is extended beyond the support is called as overhanging beam.

4. Fixed beam - A beam whose both ends are rigidly fixed in wall is called fixed beam.

5. Continuous beam - A beam which is supported on more than two supports is called continuous beam.
Type of loads:
1. Concentric or point load - A load is acting at a point is called concentric or point load.
2. Uniformly distributed load - A load which is spread on beam with uniform intensity per unit length is called uniformly distributed load or UDL.
3. Uniformly varying load - A load which is spread on beam with gradually increasing or decreasing intensity of load per unit length is called uniformly varing load or UVL.
Type of supports:
1. Movable hinge or simply or roller supports - Properties of hinge supports are below-
   a. No bending Moment.
   b. Free to rotate.
   c. Horizontal displacement is possible.
   d. No of independents of reaction copmponents – 1.
2. Immovable hinge support - Properties of hinge supports are below-
   a. Free to rotate.
   b. Both vertical and horizontal reactions.
   c. No bending moments.
   d. No of independents of reaction copmponents – 2.
3. Fixed supports - Properties of hinge supports are below-
   a. No rotation.
   b. Both vertical and horizontal reaction.
   c. Bending moments exist.
   d. No of independents of reaction copmponents – 3.
Shear Force (S.F.):
S.F. at any cross-section of the beam is the algebraic sum of vertical forces acting on left or right side of section.
Unit- Unit of shear force is N, kN, etc.
Sign conventions- Sign conventions are used as below-


Bending Moment (B.M.):
B.M. at any cross-section of the beam is the algebraic sum of moments of forces acting on left or right side of section.
Unit- Unit of shear force is N.m, kN.m, etc.
Sign conventions- Sign conventions are used as below-


Relation between SF and rate of loading:
Intensity of loading is equal to rate change of SF with respect to distance.
      Mathematically, dF/dx = W
Relation between SF and BM:
The rate of change of BM at any section is equal to the SF at that section.
      Mathematically, dM/dx = F
BM is max. at SF is zero.
if F = 0 then dM/dx = 0
Shear Force Diagram and Bending Moment Diagram (S.F.D. and B.M.D.):
S.F.D. is graphical variation of shear force along the length of beam. And B.M.D. is graphical variation of BM along the length of beam.

Point of contraflexure:
It is a point where BMD changes its sing from +ve to –ve or vice versa.
            OR
It is point at which BM is zero.
Variation of SF and BM for different loading:

               
Type of loadingSF VariationBM Variation
Point load Rectangle Inclined line for linear
UDL Linear Square Parabola
UVL Parabolic Cubic parabola
Parabolic Cubic Fourth degree polynomial
Bending couple No shear A vertical step at point of application

Horizontal Thrust Diagram (H.T.D.):
H.T.D. is diagram showing graphical variation of axial thrust along entire span.

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1 comments

  1. UnknownJuly 27, 2017 at 7:32 PM

    Why the bending moment diagram and shear force diagram is in the particular shape? Eg(rectangle, linear inclined line, parabola)

    ReplyDelete

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