EN0175-19

EN0175-19 - EN0175 11 / 09 / 06 Continue on the Airy stress...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EN0175 11 / 09 / 06 Continue on the Airy stress function method in elasticity: 2 2 = ( : Airy stress function) 2 2 y xx = , y x xy = 2 , 2 2 x yy = Example 4: P x y 1 : thickness c 2 Consider bending of a beam (height: ; thickness: 1) caused by a concentrated force at the end. The Airy stress function c 2 P 2 4 4 2 2 4 4 4 2 2 = + + = y y x x for this problem has the form: . 3 Axy = Axy y xx 6 2 2 = = , 2 2 3 Ay y x xy = = To take care of the traction free boundary on top & bottom surfaces, we can superpose a constant shear stress term to modify xy as ( ) 2 2 3 y c A xy = such that = = c y xy . The Airy stress function should be modified accordingly, xy Ac Axy 2 3 3 = The constant A is determined by the boundary condition at the end, i.e. the integral of shear stress across the section should balance the applied force P , i.e. 3 3 2 4 3 d c P A P Ay y Ac P y c c c c xy = = = Therefore: 1 EN0175 11 / 09 / 06 ( ) xy c y c P 2 2 3 3 4 = xy c P xx 3 2 3 = , ( ) 2 2 3 4 3 y c c P xy = , = yy Remark 1: P St. Venent principle: Boundary condition at the end only affects a zone of dimension on the order of beam thickness, as...
View Full Document

This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

Page1 / 7

EN0175-19 - EN0175 11 / 09 / 06 Continue on the Airy stress...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online