Axial DeformationChapter 5Lecture 1

Axially Loaded Bars

Axially Loaded Bars

Axial DeformationA structural member having a straight longitudinal axis is said to undergo axial deformation if, when loads are applied to the member or it is subjected to a temperature change:

1. The axis if the member remains straight.2. Cross section of the member remain plane, remain perpendicular to the axis, and do not rotate about the axis as the element deforms.

Axially Loaded Bars

Geometry of DeformationTheory is restricted to straight, slender members with cross section that is either constant or changes slowly along the length of the member.

Axially Loaded Bars

Kinematic AssumptionsThe axis of the member remains straight.Cross sections, which are plane and perpendicular to the axis before deformation, remain plane and perpendicular to the axis after deformation.Cross sections do not rotate.

Axially Loaded Bars

Axial DisplacementThe distance that a cross section moves in the axial direction is called its axial displacement. This displacement is labeled u(x).

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Stress Resultants

Axially Loaded Bars

Constant Normal Stress

Axially Loaded Bars

Constant Normal Stress

Axially Loaded Bars

Axial Stress

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

ExamplePart A of the bar has a 2-in diameter cross section and part B has a 4-in diameter cross section. Determine the normal stresses.

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Example

Axially Loaded Bars

ExampleThe members of the truss have equal cross sectional areas A = 400 mm2 The suspended mass is 3400 kg. Find the stress in the members.

Axially Loaded Bars

Method of Joints

Axially Loaded Bars

Method of JointsConvert mass to weight!

Axially Loaded Bars

Method of Joints

Axially Loaded Bars

Method of Joints

Axially Loaded Bars

Forces

Axially Loaded Bars

Sheet1

Member:BCBDCDCEDE

Axial Force2 mg-2.24 mg-1.33 mg2.40 mg-2 mg

Sheet2

Sheet3

Stresses

Axially Loaded Bars

Stresses

Axially Loaded Bars

Sheet1

Member:BCBDCDCEDE

Stress (Mpa)167-186-111200-167

167

-186

-111

200

-167

Sheet2

Sheet3

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars

ExampleTo test a glue, two plates are glued together as shown. The bar is formed by the joined plates and then subjected to a tensile load of 200 N. What are the normal and shear stress on the glued joint?

Axially Loaded Bars

Axially Loaded Bars

Axially Loaded Bars