What is basic influence of compressive or tensile loads on bending beams?
Compressive loads: higher bending moment —> higher deflections
Tensile loads: lower moments —> lower deflections
Why is it important, to have an engineering eye out for beams that experience a compressive/ tensile load while bending?
First order theory won´t show the influence of a compressive/ tensile load.
Only second order theory gives the additional influence.
Give the basic differential equation for the following Euler Bernoulli beam WITH an additional compressive / tensile load.
How can a compresive / tensile load be easily incorporated into the regular beam equations?
A magnification factor eta can be derrived. This magnification factor connects the first order and second order bending lines.
How can the magnification factor for bending with a compressive / tensile load be discussed?
Discussing eta is not trivial due to the high polynomial order of the influencel factors.
For the additional force approaching zero, the rule of L´Hospital is utilized, it gives a tendency to one. (No influence on the first order bending)
For the additional force approaching the critical force, the abbreviation psi approaches pi/2 which leads to the cos() in the denominator approaching 0 leading the whole term to strive towards infinity
Last changeda year ago
