Chapter 3

Shear Force and BendingMoment Diagrams in

Statically DeterminateStatically DeterminateBeams

Objectives To understand the structural behaviour of beams. To determine the effects of external loads such as axial

loads, shear force and bending moment at any section of the beam.the beam.

To derive the differential relationships between the load intensity shear force and bending moment.

To draw shear force and bending moment diagram for statically determinate beams.

Classification of statically determinate beams

Cantilever beams

Simply supported beams Simply supported beams

Overhanging beams.

Types of applied loads on the beams

Concentrated loads

Uniformly distributed loads Uniformly distributed loads

Uniformly varying loads

Externally applied moments.

Definitions Shear force: The resultant vertical force either to the right

or to the left of the section is known as shear force. Bending moment: The algebric sum of the moments of

all forces either to the left or the right at a section in a beam is known as bending moment.is known as bending moment.

Shear force diagram: A diagram in which ordinate represents shear force and abscissa represents the position of the section is called shear force diagram.

Bending moment diagram: A diagram in which ordinate represents bending moment and abscissa represents the position of the section is called bending moment diagram.

SFD and BMD for Standard Cases

1. Cantilever subjected to: a concentrated load at free end uniformly distributed load over entire span uniformly varying load over entire span

2. Simply supported beam subjected to:2. Simply supported beam subjected to: a concentrated load uniformly distributed load over entire span uniformly varying load over entire span an external moment

3. Overhanging beam subjected to a concentrated load at free end.

Nature of SF and BM variationLoad S.F. B.M.

No load Constant LinearUniformly distributed load Linear ParabolicUniformly varying Parabolic CubicUniformly varying Parabolic Cubic

Maximum shear force and bendingmoment values for standard cases

Loading Maximum Shear Force Maximum Bending Moment

W WL (fixed end)2wL

L

W

w/unit length

WL (fixed end) (fixed end)

(middle)

(right support) (load point)

(support) (middle)

2

2

wL

2

WL

WL/2

L

Wa b

4

WL

Wa

LWab

L

2

wL

L

L

w/unit length

8

hwL