File Lecture8_Slides.pdf - Mechanics of Solids Lecture 8 by...

Info iconThis preview shows pages 1–16. 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

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight 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: Mechanics of Solids Lecture 8 by Dr Emre Erkmen Lecturer, School of Civil and Environmental Engineering, The University of Technology Sydney Office: 2.520 Phone:9514 9769 Email: emre.erkmen@uts.edu.au Lecture hours: Tuesdays 11:00-14:00, Wednesdays 15:00-18:00 Office hours: Tuesdays 15:00-17:00 1 Mechanics of Solids - Lecture 8 Outline Outline- Deflections of beams- Buckling of columns 2- Torsion of circular members Mechanics of Solids - Lecture 8 Deflections Deflections are very important when designing structures and machines Load 3 STRENGTH b is related to STRESSES . SERVICEABILITY b is related to DEFLECTIONS . Mechanics of Solids - Lecture 8 Elastic Curve 4 (i) all deflections are elastic (ii) deflections due to shear are negligible and are ignored (iii) plane sections remain plane Mechanics of Solids - Lecture 8 Rotation-deflection M ( x 1 ) ( x 2 ) ( x ) ( x 2 ) 5 d tan lim d x v v x x = = x 1 x 2 1 ( x 1 ) v ( x 2 ) v d d v x = Mechanics of Solids - Lecture 8 Strain curvature relation lim lim x B A B A A B AB d y y AB x dx = = = 6 x = 2 2 d v y dx Mechanics of Solids - Lecture 8 Moment-curvature relations x x Cross-section d y x z For a linear elastic material 7 x x M E y I = = Mechanics of Solids - Lecture 8 Moment-curvature relations M EI 2 2 d v dx = M y I = x E = 8 d d v x = x d y dx = Mechanics of Solids - Lecture 8 Possible boundary conditions are shown here. Boundary Conditions v v v 9 Mechanics of Solids - Lecture 8 Cantilevered beam shown is subjected to a vertical load P at its end. Determine the elastic curve. EI is constant. Find the slope and the deflection at point A. Example-elastic curve 10 Mechanics of Solids - Lecture 8 From free-body diagram, we have the moment expression Example-elastic curve Px M = 11 By integrating twice 2 2 2 1 3 1 2 2 6 d EI Px dx d Px EI C dx Px EI C x C = = + = + + Mechanics of Solids - Lecture 8 Using boundary conditions d / dx = 0 at x = L, and = 0 at x = L , 3 1 2 2 PL C PL + = Example-elastic curve 12 2 1 6 C L C + + = Thus, C 1 = PL 2 /2 and C 2 = PL 3 /3. Mechanics of Solids - Lecture 8 Substituting these results into Eqns with = d / dx , we get ( ) 3 2 3 3 2 6 P x L x L EI = + Example-elastic curve 2 2 3 dv P L = + 13 ( ) 3 3 6 x L dx EI = = + Mechanics of Solids - Lecture 8 Example-elastic curve Determine the elastic curve. 14 Mechanics of Solids - Lecture 8 Example-elastic curve Beam is indeterminate to first degree as indicated from the free-body diagram. We can express the internal moment M in terms of the redundant force at A using segment shown below....
View Full Document

Page1 / 63

File Lecture8_Slides.pdf - Mechanics of Solids Lecture 8 by...

This preview shows document pages 1 - 16. Sign up to view the full document.

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