Reference Guide

Equation Reference 5-7
Cantilever Deflection (1, 7)
Equation:
y
P x
2
⋅
6 E I⋅ ⋅
-----------------
x 3– a⋅( )⋅
M x
2
⋅
2 E I⋅ ⋅
-----------------
w x
2
⋅
24 E I⋅ ⋅
--------------------
– 6 L
2
⋅ 4– L x⋅ ⋅ x
2
+( )⋅+=
Example:
Given: L=10_ft, E=29000000_psi, I=15_in^4, P=500_lbf, M=800_ft ∗ lbf, a=3_ft, c=6_ft, w=100_lbf/ft, x=8_ft.
Solution: y= -0.3316_in.
Cantilever Slope (1, 8)
Equation:
Θ
P x⋅
2 E I⋅ ⋅
-----------------
x 2– a⋅( )⋅
M x⋅
E I⋅
------------
w x⋅
6 E I⋅ ⋅
-----------------
– 3 L
2
⋅ 3– L x⋅ ⋅ x
2
+( )⋅+=
Example:
Given: L=10_ft, E=29000000_psi, I=15_in^4, P=500lbf, M=800_ft ∗ lbf, a=3_ft, c=6_ft, w=100_lbf/ft, x=8_ft.
Solution: Θ = -0.2652_°.
Cantilever Moment (1, 9)