Chapter 2: Statically Indeterminate - Union...
Transcript of Chapter 2: Statically Indeterminate - Union...
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 1
Chapter 2:Statically Indeterminate
DefinitionApproach
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 2
Statically Indeterminate Problems
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 3
Rules to Solve ProblemsMethod of Superposition
Decompose the statically indeterminate problem into two (or more statically determinate problems.Assumptions
The loading must be linearly related to the stress or displacement that is to be determinedThe loading must not significantly change the original geometry of the configuration or configuration of the member
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 4
Superposition MethodProcedure
Relieve the redundant constraint in the structureDetermine this structures static reactionRemove all external applied loads on the original structure and apply the redundant constraint as a pseudo-force.The solution of the original problem is arrived at by superimposing the solution from the preceding two parts through a constraint Equation
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 5
Relieve Redundant Constraint
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 6
Determine Static Reaction
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 7
Introduction of Pseudo-Force
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 8
Combine Solutions with Constraint Equation
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 9
Example 1Consider a steel rod that has a diameter of 5mm. It is attached to a fixed wall at A, and before it is loaded there is a gap between the wall at B’ and the rod of 1mm. Determine the reaction at A and B’ if the rod is subject to an axial force of P=20kN as shown. Neglect the size of the collar at C. E=200 GPa
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 10
Example 2The ends of the 15mm diameter steel rods “BE”and “CD” are single threaded with a pitch of 2.25mm. Knowing that after being snugly fitted, the nut at C is tightened one full turn, determine (a) the tension in rod “CD”, (b) the deflection of point “C”of the rigid member “ABC”. The elastic modulus of steel is 200GPa.
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 11
Kinematic Constraint
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Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 12
Implication of tightening the nut one more turn.