SME
Structural Analysis · Problem type
A cantilever: the wall’s shear and moment
Use this for “A 3 m cantilever carries 10 kN at its tip and 4 kN/m along it. Find the shear and moment at the wall.”
Diagram
ΣF = 0: RA = 22 kN, the total load.
The wall at A holds MA = 48 kN·m, counterclockwise.
|M| is largest at x = 0 m: −48 kN·m.
The area under V between two points is the change in M.
This is an example. Type your own values to start a new problem.
V (kN)
=
P (kN)
+
w (kN/m)
×
L (m)
M (kN·m)
=
P (kN)
×
L (m)
+
w (kN/m)
×
(
L (m)
)
2
÷
2
Formulas
V
=
P
+
w
×
L
22 = 10 + 4 × 3
M
=
P
×
L
+
w
×
L
2
2
48
=
10
×
3
+
4
×
3
2
2
Assumptions
•
Fixed at the wall A, free at the tip; w covers the whole length and includes the beam’s weight.
•
Every load pushes down; the fixed-end moment is the largest moment, and it bends the beam hogging.
Step-by-step
WE KNOW
P = 10 kN, w = 4 kN/m, L = 3 m
FIND
shear at the wall (V), moment at the wall (M)
Step 1 · Find shear at the wall (V)
Use V = P + w × L
The
wall
holds
up
every
load:
P
and
the
whole
wL.
V
=
10
+
4
×
3
V
=
10
+
12
V
=
22
kN
Step 2 · Find moment at the wall (M)
Use M = P × L + w × L² ÷ 2
Moments
about
the
wall:
P
at
arm
L
,
and
wL
at
arm
L
2
.
M
=
10
×
3
+
4
×
3
2
2
M
=
10
×
3
+
4
×
9
2
M
=
30
+
36
2
M
=
30
+
18
M
=
48
kN·m
Check
Put the numbers back in. Both sides should match.
22 = 10 + 4 × 3 ✓
48
=
10
×
3
+
4
×
3
2
2
✓
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Shear and moment of a uniform load
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Truss member force by the method of sections
Topic check
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