Simple Deflection (1, 3)

Equation:

y =

P--------------------------------⋅

( L – a ) ⋅ x

⋅ ( x 2

+ ( L – a ) 2 – L 2 )

 

 

6

⋅ L ⋅

E

⋅

I

 

 

 

 

 

 

–

M

⋅ x

⋅

c

– ----------

x 2

L

– ----------

c 2

 

------------E

⋅ I

⋅ L

– ---

⋅ L

 

 

 

 

6

3

2

 

–

24--------------------

w ⋅ x

⋅

I

⋅ ( L 3 + x 2 ⋅ ( x – 2 ⋅ L ) )

 

 

⋅ E

 

 

 

 

 

 

 

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:

ΘP ⋅ (L – a) ⋅ ( ⋅ 2 ( )2 2)

=------------------------- 3 x + L – a – L 6 ⋅ L ⋅ E ⋅ I

M

x2

L

 

c2

–E----------⋅ I ⋅

c –

2-----------⋅ L –

---3

–

2-----------⋅ L 

–--------------------

w

⋅ (L3 + x2

⋅ (4 ⋅ x – 6 ⋅ L) )

24

⋅ E ⋅ I

 

 

 

 

Equation Reference 5-5