Lecture Strength of Materials I: Chapter 3 - PhD. Tran Minh Tu

Axially loaded members are structural components subjected only to axial force (tension or compression).. • Prismatic bar: Straight structural member with the same cross- section through[r]

STRENGTH OF MATERIALS

CHAPTER

Axially loaded

members

3.1 Introduction 3.2.Normal Stress and Normal Strain 3.3 Tension and Compression Test 3.4 Poisson’s ratio

3.5 Shearing Strain 3.6 Allowable Stress – Factor of Safety 3.7 Statically Indeterminate Problem

3.1 Introduction

• Suitability of a structure or machine may depend on the deformations in the structure as well as the stresses induced under loading Statics analyses alone are not sufficient

• Considering structures as deformable ones allows us to determinate the member forces and reactions which are statically indeterminate.

• Determination of the stress distribution within a member also requires the consideration of deformations in the member

• Chapter 3 is concerned with the stress and deformation of a

3.1 Introduction

Axially loaded members are structural components subjected only to axial force (tension or compression)

• Prismatic bar: Straight structural member with the same cross-section throughout its length

• Axial force: Load directed along the axis of the member

• Axial force can be tensile or compressive

3.1 Introduction

3.1 Introduction

 Axial force diagram

0 z



Using the method of section , the internal axial force is obtained from the equilibrium as a function of coordinate z

 Kinematic assumptions Before deformation

After deformation

 Kinematic assumptions

3.2 Normal stress and normal strain

 Normal stress

z z

N A

 

z const

 

 – normal stress at any point on

the cross-sectional area

Nz – internal resultant normal force

1 The axis of the member remains straight

2 Cross sections which are plane and are perpendicular to the axis before deformation, remain plane and remain perpendicular to the axis after deformation And the cross sections do not rotate about the axis

3.2 Normal stress and normal strain

 Elongation of the bar:

Consider the bar, which has a cross-sectional area that gradually varies along its length L The bar is subjected to concentrated loads at its ends and variable external load distributed along its length

0

( ) ( )

L

N z dz L

EA z



   

3.2 Normal stress and normal strain

 Elongation of the bar – constant load

and cross-sectional area:

z

N L L

EA



  

z

N

L EA



 Normal Strain – elongation per unit

length

EA – stiffness of axially loaded bar