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

Simply Supported Beams
Beam Slope Deflection Elastic Curve
v
1 x
θ 1
θ 2
v max
L
L
—
2
P
—
2
2
PL
θ1 =− θ2
=− v
16EI
max
=−
3
PL
48EI
v
Px
=− (3 L 2 − 4 x
2 )
48 EI
for 0
≤ x ≤
L
2
2
v
θ 1
a
L
P
θ 2
b
x
θ =−
1
θ =+
2
2 2
Pb ( L − b )
6 LEI
2 2
Pa ( L − a )
6 LEI
v
=−
2 2
Pa b
3LEI
x a at =
v
Pbx
2 2 2
=− ( L − b − x )
6 LEI
x a
for 0≤ ≤
v
M
3 x
θ θ
1
2
L
θ 1 =−
θ 2 =+
ML
3EI
ML
6EI
v
max
=−
at x = L 1 −
⎛
⎝
⎜
2
ML
9 3EI
3
3
⎞
⎠
⎟
v
Mx
=− (2 L 2 − 3 Lx + x
2 )
6 LEI
v
w
4 x
θ 1
θ 2
v max
L
L
—
2
—
2
3
wL
θ1 =− θ2
=− v
24EI
max
5
384
wL
EI
4
=− v
wx
=− ( L 3 − 2 Lx 2 + x
3 )
24 EI
5
v
v
w 2
wa
θ 1 =− (2 L − a)
24 LEI
θ θ
1
2
a
L
6 x
θ 1
θ 2
L
x
2
wa
2 2
θ 2 =+ (2 L − a )
24 LEI
w 7 wL 0 3
0 θ 1 =−
360 EI
θ =+
2
wL 0 3
45EI
2
v
3
wa
2 2
=− (4 L − 7aL + 3 a )
24 LEI
v
max
=−
x a at =
0.00652
at x = 0.5193 L
wL
EI
0 4
v
v
wx
=− ( Lx − 4aLx + 2 a x
24 LEI
3 2 2 2
2 2 3 4
+ 4aL − 4 aL + a )
x a
for 0≤ ≤
2
wa
3 2 2
=− (2 x − 6 Lx + a x
24 LEI
2 2
+ 4 Lx − aL)
v
a x L
for ≤ ≤
wx
=− 0 (7 L 4 − 10 L 2 x 2 + 3 x
4 )
360 LEI
822