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A longitudinal deformation (in the direction of the axis) is called elongation. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load.
For thick plates, we have to consider the effect of through-the-thickness shears on the orientation of the normal to the mid-surface after deformation. Raymond D. Mindlin's theory provides one approach for find the deformation and stresses in such plates. Solutions to Mindlin's theory can be derived from the equivalent Kirchhoff-Love solutions ...
The design of tension members requires careful analysis of potential failure modes, specifically yielding (excessive deformation) and fracture, which are referred to as limit states. The governing limit state is the one that results in the lowest design strength, as it dictates the member's capacity and prevents structural failure.
In other words, any deformation due to shear across the section is not accounted for (no shear deformation). Also, this linear distribution is only applicable if the maximum stress is less than the yield stress of the material. For stresses that exceed yield, refer to article plastic bending.
The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium. A load beyond the critical load causes the column to fail by buckling. As the load is increased beyond the ...
The curve () describes the deflection of the beam in the direction at some position (recall that the beam is modeled as a one-dimensional object). q {\displaystyle q} is a distributed load, in other words a force per unit length (analogous to pressure being a force per area); it may be a function of x {\displaystyle x} , w {\displaystyle w ...
Physically, taking into account the added mechanisms of deformation effectively lowers the stiffness of the beam, while the result is a larger deflection under a static load and lower predicted eigenfrequencies for a given set of boundary conditions. The latter effect is more noticeable for higher frequencies as the wavelength becomes shorter ...
Dead loads have small load factors, such as 1.2, because weight is mostly known and accounted for, such as structural members, architectural elements and finishes, large pieces of mechanical, electrical and plumbing (MEP) equipment, and for buildings, it's common to include a Super Imposed Dead Load (SIDL) of around 5 pounds per square foot ...