Mechanics of Solids 3 min read
Internal Forces and Moments in Beams
A beam is a structural element like the truss member but, unlike the latter, it is designed, fabricated, and assembled…
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Mechanics of Solids 3 min read
Internal Forces in Members of a Truss Structure
We are ready to start talking business, to buy a loaf of bread. Up until now we have focused on…
Mechanics of Solids 3 min read
Static Equilibrium Force and Moment
The correct response is zero: For a particle at rest, or moving with constant velocity relative to an inertial frame,…
Mechanics of Solids 3 min read
Equations of motion of linear elastic bodies
The final equations of the purely mechanical theory of linear elasticity (i.e., when coupling with the temperature field is neglected,…
Mechanics of Solids 4 min read
Finite elastic deformations
When elastic response under arbitrary deformation gradients is considered—because rotations, if not strains, are large or, in a material such…
Mechanics of Solids 3 min read
Thermodynamic considerations
In thermodynamic terminology, a state of purely elastic material response corresponds to an equilibrium state, and a process during which…
Mechanics of Solids 3 min read
Thermal strains
Temperature change can also cause strain. In an isotropic material the thermally induced extensional strains are equal in all directions,…
Mechanics of Solids 2 min read
Stress-strain relations
Linear elastic isotropic solid The simplest type of stress-strain relation is that of the linear elastic solid, considered in circumstances…
Mechanics of Solids 2 min read
Finite deformation and strain tensors
In the theory of finite deformations, extension and rotations of line elements are unrestricted as to size. For an infinitesimal…
Mechanics of Solids 3 min read
Small-strain tensor
The small strains, or infinitesimal strains, εij are appropriate for situations with |∂uk/∂Xl|<< 1 for all k and l. Two…
Mechanics of Solids 3 min read
Geometry of deformation
Strain and strain-displacement relations The shape of a solid or structure changes with time during a deformation process. To characterize…
Mechanics of Solids 3 min read
Equations of motion
Now the linear momentum principle may be applied to an arbitrary finite body. Using the expression for Tj above and…
