University of Alberta

CIVE 270

AXIAL FORCE, SHEAR FORCE, AND BENDING MOMENT DIAGRAMS
1.1 Step by Step Procedure
1. Select a Free Body - i.e. isolate beam or portion of it.
2. Draw the Free Body Diagram
(i) draw the free body
(ii) identify all known forces
(iii) identify all possible unknown reactions
(iv) label and dimension diagram
3. Determine Reactions
(i) from the free body diagram, set up the equations of statics,
ΣF
x
= 0, ΣF
y
= 0, ΣM = 0.
(ii) solve for the unknown reactions
(iii) check solution
4. Using the method of sections and/or load, shear force and bending moment
relationships, draw the shear force an bending moment diagrams.
The method of sections uses statics to examine a free body to the left or right of any
section to determine the axial force, shear force and bending moment at the section.
1.2 Relationships Among Load, Shear and Bending Moment
1.2.1 Load, Shear Force Relationships
(i) The slope of the shear force diagram is equal to the load intensity:
Laboratory 1 Civ E 270 2
dV
dx
= - w
(ii) The change in shear between two locations x1 and x2 along the beam is equal
to the area under the load diagram between x1 and x2
V x V x w dx
x x
( ) ( ) 2 1
2 1
- = - ∫