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

cantilever Beams
Beam Slope Deflection Elastic Curve
7
v
P
vmax
x
2
PL
θ max =− v
2EI
max
3
PL
=− v
3EI
2
Px
=− (3 L − x)
6 EI
L
θmax
v
P
8 x
vmax
L
L
—
2
—
2
θmax
2
PL
θ max =− v
8EI
max
=−
5
48
PL
EI
3
v
v
2
Px
=− (3 L − 2 x) for 0 ≤ x ≤
12 EI
2
PL
L
=− (6 x − L) for ≤ x ≤ L
48 EI
2
L
2
v
9
M
x
v max
ML
θ max =− v
EI
max
2
ML
=− v
2EI
=−
Mx
2EI
2
L
θmax
10
v
w
L
v max
θ max
x
3
wL
θ max =− v
6EI
max
4
wL
=− v
8EI
2
wx
2 2
=− (6 L − 4 Lx + x )
24 EI
11
v w 0
wL 0 3
x θ max =− v
24EI
L
v max
θ max
max
wL 0 4
=− v
30EI
wx 0 2
=− (10L 3 − 10L 2 x + 5 Lx 2 − x
3 )
120 LEI
823