File Lecture2_Slides.pdf - Mechanics of Solids Lecture 2 by...

Info iconThis preview shows pages 1–10. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mechanics of Solids Lecture 2 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 2 Outline Outline- Poisson’s ratio- Stress and deformation in axially loaded members - Principle of superposition - Statically indeterminate axially loaded members - Composite axially loaded members 2 Mechanics of Solids - Lecture 2 • When a body is subjected to axial tensile force, it elongates and laterally contracts • Similarly, when it is subjected to an axial compressive force its sides expand laterally Poisson’s ratio 3 Mechanics of Solids - Lecture 2 • Strains of the bar are: ε long = δ L ε lat = δ’ r Poisson’s ratio Poisson’s ratio Poisson’s ratio, ν = − ε lat ε long • Early 1800s, Poisson realized that within elastic range, ratio of the two strains is a constant value, since both are proportional. 4 Mechanics of Solids - Lecture 2 • Why negative sign? Longitudinal elongation cause lateral contraction and vice versa • Lateral strain is the same in all lateral (radial) directions Poisson’s ratio Poisson’s ratio • Poisson’s ratio is dimensionless, 0 ≤ ν ≤ 0.5 • Poisson’s ratio is unique for homogenous and isotropic material 5 Homogenous material : The material has the same composition everywhere Isotropic material : The material has the same behaviour in all directions In the elastic range we will be using the three material constants that we have learnt so far, i.e. E modulus of elasticity, G shear modulus and ν Poisson’s ratio throughout this course Mechanics of Solids - Lecture 2 Bar is made of A-36 steel and behaves elastically. Determine change in its length and change in dimensions of its cross section after load is applied. Example 6 Mechanics of Solids - Lecture 2 Normal stress in the bar is rom tables, 200 GPa, strain in irection is Example P A σ = 3 2 80 10 16 50 100 N MPa mm × = = × From tables, E = 200 GPa, strain in z-direction is Axial elongation of the bar is, 7 E σ ε = 6 16 80 10 200 MPa GPa − = = × 6 80 10 1.5 L m δ ε − = = × × 120 m μ = Mechanics of Solids - Lecture 2 Using ν st = 0.32, contraction strains in both x and y directions are Example 6 0.32 80 10 x y z ε ε ν ε − = = − = − × × 25.6 m m μ = − Thus changes in dimensions of cross-section are 8 6 25.6 10 0.1 2.56 x x x z L m m δ ε ν ε μ − = = − = − × × = − 6 25.6 10 0.05 1.28 y y y z L m m δ ε ν ε μ − = = − = − × × = − Mechanics of Solids - Lecture 2 Principle of superposition P=P 1 +P 2 L P 1 P 2 L L The effect of a combined loading can be obtained by determining the effects of each load separately and combining the results 9 After applying the first load P 1 , we did not consider the length of the bar as 1 L δ + Why?...
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 / 60

File Lecture2_Slides.pdf - Mechanics of Solids Lecture 2 by...

This preview shows document pages 1 - 10. Sign up to view the full document.

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