Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Table 7.1 construction Rules for Shear-Force and Bending-moment Diagrams
Equation load Diagram w Shear-Force Diagram V Bending-Moment Diagram M
Rule 1: Concentrated loads create discontinuities in the shear-force diagram. [Equation (7.5)]
∆V = P 0
Positive jump
Slope = V
P B
0
in shear force V
M A M B
V B
Slope = V
P A
M
0
B
V
x A x 0 x A
B
M A
V A
V B
x A x 0 x B
x A x 0 x B
Rule 2: The change in shear force is equal to the area under the distributed-load curve. [Equation (7.3)]
B
V − V = wxdx ( )
B
A
∫
x
xA
xB
w(x) dx
x
A
w(x)
M A
x A x B
M B
∆V = V B – V A =
V A
∆V
xB
w(x) dx
x
A
V B
M A
x A
x B
MB
V A
V B
x A
x B
Rule 3: The slope of the V diagram is equal to the intensity of the distributed load w. [Equation (7.1)]
dV
dx
=
wx ( )
M A
x A x B
M B
w A
w B
x A x B
V A
Slope = w B
Slope = w
V B A
1
w A
1
w B
M A
x A
x B
MB
V A
V B
Rule 4: The change in bending moment is equal to the area under the shear-force diagram. [Equation (7.4)]
B
M − M = Vdx
B
A
∫
x
xA
w
M A M B
x A x B
V A
V B
V A
xB
V(x) dx
x
A
V B
∆M = MB
– M A =
∆M
M A
xB
V(x) dx
x
A
MB
x A
x B
x A
x B
Rule 5: The slope of the M diagram is equal to the intensity of the shear force V. [Equation (7.2)]
dM
dx
= V
w
M A M B
x A x B
V A
V B
V A
x A
Slope = w
x B
V B
M A
x A
1
Slope = V B
Slope = VA
V A
MB
x B
1
V B
Rule 6: Concentrated moments create discontinuities in the bending-moment diagram. [Equation (7.6)]
M A
x A x B
∆ M = −M 0
M B
VA
No effect on
shear force V
V B
M A
Negative jump in
bending moment
M 0
MB
V A
M 0
V B
x A
x B
x A x 0 x B
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