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Chapter 27

Energy Methods

Strain Energy
Strain Energy
Consider a rod fixed at one end and subjected to an axial force at the free end, which induces stress and leads to elongation in the rod.  As the ...
Strain-Energy Density
Strain-Energy Density
An axial load causes a rod to elongate, and store strain energy in it. The strain energy density in the rod is the energy per unit volume. Here, the ratio ...
Elastic Strain Energy for Normal Stresses
Elastic Strain Energy for Normal Stresses
When a material is subjected to an axial loading, it experiences normal stress, leading to strain energy generation. This equation is valid for uniformly ...
Elastic Strain Energy for Shearing Stresses
Elastic Strain Energy for Shearing Stresses
When the material is subjected to a shearing stress, the strain energy density can be expressed in integral form as the product of the shearing stress and ...
Impact Loading
Impact Loading
Consider a rod of uniform cross-sectional area fixed at one end. When another moving object hits the free end of the rod, the rod deforms, and stress is ...
Impact Loading on a Cantilever Beam
Impact Loading on a Cantilever Beam
Consider a cantilever beam fixed at one end, having a circular cross-section. If an object is dropped on the free end of the cantilever from a height h, ...
Castigliano's Theorem
Castigliano's Theorem
Castigliano's theorem is useful for determining displacements and rotations in structures undergoing elastic deformations. It states that the partial ...
Castigliano's Theorem: Problem Solving
Castigliano's Theorem: Problem Solving
Consider a simply supported beam PQ of length L, carrying a point load F at the center. What will be the deflection at the center of the beam? Here, the ...
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