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$\delta = \dfrac{PL}{AE} = \dfrac{\sigma L}{E}$ 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 ...
- Solution to Problem 205 Axial Deformation
Problem 205 A uniform bar of length L, cross-sectional area...
- Shearing Deformation
Shearing Deformation Shearing forces cause shearing...
- Stress-strain Diagram
Suppose that a metal specimen be placed in...
- Simple Strain
Also known as unit deformation, strain is the ratio of the...
- Thermal Stress
where α is the coefficient of thermal expansion in m/m°C, L...
- Non-uniform Cross-section
$\delta = \dfrac{PL}{AE} = \dfrac{\sigma L}{E}$ To use this...
- Solution to Problem 205 Axial Deformation
Calculation of the elastic response spectrum in terms of spectral acceleration and spectral displacement representing the seismic action in the horizontal or vertical direction. Applicable for the design of structures that remain in the elastic range, seismic isolation systems, and calculation of seismic displacements.
The expression for deformation and a given load \(\delta = PL/AE\) applies just as in tension, with negative values for \(\delta\) and \(P\) indicating compression.
Displacement diagram (to Scale) Horizontal Displacement = PL AE to the left vertical displacement = 12.9 PL AE
You're trying to find the displacement of the bar with the load distributed longitudinally at a point A. You use the formula displacement = PL/AE where P=load, L=length of member, A=cross-sectional area tangent to the load, and E=Young's modulus.
\(\delta_P = \dfrac{PL^3}{48EI}\) where the length \(L\) and the moment of inertia \(I\) are geometrical parameters. If the ratio of \(\delta_P\) to \(P\) is measured experimentally, the modulus \(E\) can be determined. A stiffness measured this way is called the flexural modulus.
• Determine the relative displacement of the free end at A with respect to the fixed end at D. The modulus of elasticity for aluminum is 10 x 10 6 psi • Solve the problem using the ( a)discrete element method, and (b) the superposition method.