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]
(1)(2)3
CHAPTER
(3)Contents
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
(4)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.
(5)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
(6)(7)3.1 Introduction
Axial force diagram
0 z
Z N
Using the method of section , the internal axial force is obtained from the equilibrium as a function of coordinate z
Kinematic assumptions Before deformation
(8) 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
(9)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
(10)3.2 Normal stress and normal strain
Elongation of the bar – constant load and cross-sectional area:
z N L L EA z N
Normal Strain – elongation per unit
length