SLIDE 1
1
Wednesday, Sept. 5 CIVL 7166 1
Stresses Due to Point Load
z r R P
( ) ( )
⎡ ⎤ σ = ⎢ ⎥ π ⎣ ⎦ ⎡ ⎤ σ = − − υ ⎢ ⎥ π + ⎣ ⎦ ⎡ ⎤ σ = − υ − ⎢ ⎥ π + ⎣ ⎦
3 z 2 3 2 r 2 3 t 2
P z 2 R R P 3r z R 1 2 2 R R R z P R z 1 2 2 R R z R
Wednesday, Sept. 5 CIVL 7166 2
Stresses Due to Circular Load
q 2a z
( ) ( )
⎡ ⎤ ⎛ ⎞ ⎢ ⎥ σ = − ⎜ ⎟ ⎢ ⎥ + ⎝ ⎠ ⎣ ⎦ ⎡ ⎤ ⎛ ⎞ + υ ⎢ ⎥ σ = + υ − + ⎜ ⎟ ⎢ ⎥ + + ⎝ ⎠ ⎣ ⎦ ⎡ ⎤ ⎛ ⎞ + υ ⎢ ⎥ σ = + υ − + ⎜ ⎟ ⎢ ⎥ + + ⎝ ⎠ ⎣ ⎦
3 z 2 2 3 r 2 2 2 2 3 t 2 2 2 2
z q 1 a z 2 1 z q z 1 2 2 a z a z 2 1 z q z 1 2 2 a z a z
Wednesday, Sept. 5 CIVL 7166 3
Hooke’s Law
( ) ( ) ( )
⎡ ⎤ ε = σ − ν σ + σ ⎣ ⎦ ⎡ ⎤ ε = σ − ν σ + σ ⎣ ⎦ ⎡ ⎤ ε = σ − ν σ + σ ⎣ ⎦
z z r t r r z t t t r z