{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HomeWork4

# HomeWork4 - Home Work 4 y 10 h=1 o x 45o 10 A B 12 C(a...

This preview shows pages 1–4. Sign up to view the full content.

Home Work # 4 (a) Consider the stress function, 3 xy φ = . (1) Compute the corresponding stresses. (2) Show on the sketch the sense and magnitude of the boundary forces at point A and along the edge BC . (3) Compute the displacements u and v of point C relative to point o . Assume no rigid body motion. (b) Compute Airy’s stress function, φ , and plot the boundary values for the following loadings: 10" 10" A 12" C 45 o o B x y 1 h = ( 29 2 x y p p 2 b 2 a ( 29 ( 29 ( 29 3 1 2 + M M ( 29 1 ( 29 4 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Solution (a) (1) Compute the stresses 2 2 6 x xy y φ σ = = , 2 0 y x φ σ = = , 2 3 xy y x y φ τ = - = - ∂ ∂ (2) Sketch boundary forces at A and along BC. from Eq. (3-11) 2 2 2 2 2 2 dy dx x y ds x y ds dx dy y x ds x y ds φ φ φ φ = + ∂ ∂ = - - ∂ ∂ 2 2 2 2 10 10 for A , , third quadrant , 2 2 1 1 10 10 1 10 1 6 3 6 3 75 2 2 2 2 2 2 2 2 1 10 1 3 3 75 2 2 2 2 A A dx dy x y ds ds x xy y y y = - = - ⇒ + ⇒ -     = - + = - - - + - = -           = - - = - - - =     ( 29 ( 29 ( 29 2 for BC / 0, / 1 6 0 3 1 300 0 B C B C dy ds dx ds x xy y y - - = = = + = = (3) ( 29 ( 29 2 1 2 2 6 6 - - - - - (a) 6 6 - - - - (b) from (a), 3 from (b), 3 y x x y x y u xy u E xy x E E E x v xy v E xy y E E E y Eu x y g y Ev x y g x μσ σ ε σ μσ ε μ μ μ = = - = = = = - = - = - = + = - + 2
( 29 ( 29 2 2 1 2 1 3 3 - - - - (c) xy u v x g y y g x y x E γ μ + = = + - + from linear elasticity, ( 29 ( 29 2 2 1 6 1 - - - - ( ) xy xy xy y u v d G E y x E τ τ μ μ γ + + = = = + = - from ( c ) and ( d ) ( 29 ( 29 ( 29 ( 29 2 2 2 2 1 3 6 3 0 x g x y y g y F

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 9

HomeWork4 - Home Work 4 y 10 h=1 o x 45o 10 A B 12 C(a...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online