Reference Guide
Equation Reference 5-5
Simple Deflection (1, 3)
Equation:
y
P L a–( ) x⋅ ⋅
6 L E I⋅ ⋅ ⋅
--------------------------------
x
2
L a–( )
2
L
2
–+( )⋅=
M x⋅
E I⋅
------------
– c
x
2
6 L⋅
-----------
–
L
3
---
–
c
2
2 L⋅
-----------
–
⋅
w x⋅
24 E I⋅ ⋅
--------------------
– L
3
x
2
x 2– L⋅( )⋅+( )⋅
Example:
Given:
L=20_ft, E=29000000_psi, I=40_in^4, a=10_ft, P=674.427_lbf, c=17_ft, M=3687.81_ft
∗
lbf,
w=102.783_lbf/ft, x=9_ft.
Solution:
y= -0.6005_in.
Simple Slope (1, 4)
Equation:
Θ
P L a–( )⋅
6 L E I⋅ ⋅ ⋅
-------------------------
3 x⋅
2
L a–( )
2
L
2
–+( )⋅=
M
E I⋅
----------
– c
x
2
2 L⋅
-----------
–
L
3
---
–
c
2
2 L⋅
-----------
–
⋅
w
24 E I⋅ ⋅
--------------------
– L
3
x
2
4 x⋅ 6– L⋅( )⋅+( )⋅