Cantilever Deflection (1, 7)

Equation:

y =

P ⋅ x2

⋅ (x – 3 ⋅ a) +

M ⋅ x2

–

--------------------w ⋅ x2

⋅ (6 ⋅ L

2

– 4 ⋅ L ⋅ x + x

2

)

6-----------------

⋅ E ⋅ I

2-----------------

 

⋅ E ⋅

 

 

 

 

⋅ E ⋅ I 24

I

 

 

 

 

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

⋅ (x – 2 ⋅ a) +

M------------⋅ x – -----------------

w ⋅ x

⋅ (3 ⋅ L2

– 3 ⋅ L ⋅ x + x2)

2

⋅ E ⋅ I

 

E ⋅ I 6

⋅ E ⋅

I

 

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)

Equation Reference 5-7