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We determine the constants of integration by evaluating our expression for displacement v(x) and/or our expression for the slope dv/dx at points where we are sure of their val-ues. One such boundary condition is that, at x=0 the displacement is zero, i.e., vx()= 0 x = 0 Another is that, at the support point B, the displacement must vanish, i.e.,
Displacement diagrams are effectively plotting the displacement vectors of the joints as defined by the end of the bars. The displacement vector for the end of a bar is made up of two components: (1) an extension, of a magnitude defined by the bar force and the constitutive behavior of the bar which is parallel to the direction of the bar and (2) a
PL AE: (1.5) While this formulation is quite simplified, computation of stress for 3D solids with loads in multiple directions will be more complex. To illustrate this, and for the sake of completeness, while force is a vector (it has magnitude and direction), i.e., a first-order tensor, stress is a second-order tensor, which is a
From the relationship between stress, strain, and displacement, we can derive a 3D elastic wave equation. Figure 1.1 shows relationships between each pair of parameters. In this section, I will show each term in Figure 1. 1.1.1 Displacement Displacement, characterizes vibrations, is distance of a particle from its position of equilibrium: u(x,t ...
the load will be proportional to displacement. σ = P/A δ = PL/AE 2. The geometry of the structure must not undergo significant change when the loads are applied, i.e., small displacement theory applies. Large displacements will significantly change and orientation of the loads. An example would be a cantilevered thin rod subjected to a force ...
Displacement diagram (to Scale) Horizontal Displacement = PL AE to the left vertical displacement = 12.9 PL AE
$\delta = \dfrac{PL}{AE} = \dfrac{\sigma L}{E}$ To use this formula, the load must be axial, the bar must have a uniform cross-sectional area, and the stress must not exceed the proportional limit. If however, the cross-sectional area is not uniform, the axial deformation can be determined by considering a differential length and applying ...
