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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