Beams Overview

BeamsShear & Moment Diagrams

Beams

• Members that are slender and support loads applied perpendicular to their longitudinal axis.

Span, L

Distributed Load, w(x) Concentrated Load, P

Longitudinal Axis

Types of Beams

• Depends on the support configuration

M

Fv

FHFixed

FV FV

FH

Pin

Roller

PinRoller

FVFV

FH

Statically Indeterminate Beams

• Can you guess how we find the “extra” reactions?

Continuous Beam

Propped Cantilever Beam

Internal Reactions in Beams

• At any cut in a beam, there are 3 possible internal reactions required for equilibrium: – normal force, – shear force, – bending moment.

L

P

a b



Pb/Lx

Left Side of Cut

V

M

N

Positive Directions Shown!!!



Pa/L

L - x

Right Side of CutVM

N

Positive Directions Shown!!!

Finding Internal Reactions• Pick left side of the cut:

– Find the sum of all the vertical forces to the left of the cut, including V. Solve for shear, V.

– Find the sum of all the horizontal forces to the left of the cut, including N. Solve for axial force, N. It’s usually, but not always, 0.

– Sum the moments of all the forces to the left of the cut about the point of the cut. Include M. Solve for bending moment, M

• Pick the right side of the cut:– Same as above, except to the right of the cut.

dx)x(V)x(M

dx)x(w)x(V

functionloadthe)x(w

The Relationship Between Load, Shear and Bending Moment

Load

0 Constant Linear

Shear

Constant Linear Parabolic

Moment

Linear Parabolic Cubic

Common Relationships

Load

0 0 Constant

Shear

Constant Constant Linear

Moment

Linear Linear Parabolic

Common Relationships

M

Example: Draw Shear & Moment diagrams for the following beam

3 m 1 m1 m

12 kN 8 kNA C

B

D

RA = 7 kN RC = 13 kN

3 m 1 m1 m

12 kNA C

B

D

V(kN)

M(kN-m)

7

-5

8

8 kN

7

-15

8

7

-82.4 m

Documents

Beams Overview