File - Mechanics of Solids Lecture 6 by Dr Emre Erkmen Lecturer School of Civil and Environmental Engineering The University of Technology Sydney

Info iconThis preview shows pages 1–13. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mechanics of Solids Lecture 6 by Dr Emre Erkmen Lecturer, School of Civil and Environmental Engineering, The University of Technology Sydney Office: 2.520 Phone:9514 9769 Email: [email protected] Lecture hours: Tuesdays 11:00-14:00, Wednesdays 15:00-18:00 Office hours: Tuesdays 15:00-17:00 1 Mechanics of Solids - Lecture 6 Outline Outline- Combined bending and axial load- Composite beams under bending moment 2 Mechanics of Solids - Lecture 6 Normal force N causes: uniform normal stress Bending moment M causes: linear longitudinal stress distribution Members under combined bending moment and axial force N A σ = M y I σ = − N σ σ M Resultant stresses by superposition: Use the principal of superposition to determine the resultant normal stress distribution N M y A I σ = − M N Mechanics of Solids - Lecture 6 Eccentric force x e P ide view of the beam x P = M=Pe x e P = + P P y 4 • An eccentric load P can be replaced by a centric load P and a couple M = Pe. • Normal stresses can be found from superposing the stresses due to the centric load and couple. centric bending P M y A I σ σ σ σ = + = + − Tensile force Compression above neutral axis From the formula P P e y A I × = − M P e = × Mechanics of Solids - Lecture 6 Eccentric force x e P x P M=Pe = y 5 • Normal stresses centric bending P M y A I σ σ σ σ = + = − − Compressive force From the formula M P e = × P P e y A I × = − − Mechanics of Solids - Lecture 6 Eccentric force x e P x P M=-Pe = y x P M=Pe = 6 • Normal stresses centric bending P M y A I σ σ σ σ = + = + − Tensile force From the formula M P e = − × P P e y A I × = + + Mechanics of Solids - Lecture 6 Eccentric force x e P Side view of the beam x P = M=-Pe y 7 • Normal stresses can be found from superposing the stresses due to the centric load and couple. centric bending P M y A I σ σ σ σ = + = − − Compressive force Compression above neutral axis From the formula P P e y A I × = − + M P e = − × Mechanics of Solids - Lecture 6 Internal forces under combined axial force and bending moment N=P C 8 M=P.e x N My A I σ = − − y N.A Neutral axis not passing from centroid Mechanics of Solids - Lecture 6 Neutral axis and maximum stress under eccentric force x e P x P M=Pe = y + y 9 • Neutral axis is where the normal stress is zero. P P e y A I σ × = − = N P P e y A I σ × = − N I y A e = × Mechanics of Solids - Lecture 6 Neutral axis and maximum stress under eccentric force x e P x P M=Pe = y + y 10 P P e y A I σ × = − − N I y A e = − × • Neutral axis is where the normal stress is zero. N P P e y A I σ × = − − = Mechanics of Solids - Lecture 6 Neutral axis and maximum stress under eccentric force x e P = y x P M=Pe = y N 11 N P P e y A I σ × = + N I y A e = − × P P e y A I σ × = + = • Neutral axis is where the normal stress is zero. Mechanics of Solids - Lecture 6 Neutral axis and maximum stress under eccentric force x e P x P = M=Pe y 12 N P...
View Full Document

This note was uploaded on 08/22/2011 for the course ENG 48331 taught by Professor Brown during the Three '11 term at University of Technology, Sydney.

Page1 / 73

File - Mechanics of Solids Lecture 6 by Dr Emre Erkmen Lecturer School of Civil and Environmental Engineering The University of Technology Sydney

This preview shows document pages 1 - 13. Sign up to view the full document.

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