What is bending ? How bending problems prevents and what is buckling ?
What is bending ? How bending problems prevents and what is buckling ?
A bridge has to be designed such that it can withstand the load of the flowing traffic, the force of winds and its own weight. Means it should not bend too much or break.
Similarly, in the design of building use of beams and column is very common.
In both the cases, the overcoming of the problem of bending of beam under a load is important.
Let us consider the case of a beam loaded at the centre and supported near its ends as shown in figure $(a)$.
A bar of length $l$, breadth $b$ and depth $d$ when loaded at the centre by a load $\mathrm{W}$ sags by an amount given by,
$\delta=\frac{\mathrm{W} l^{3}}{4 b d^{3} \mathrm{Y}}$
where $\mathrm{Y}=$ Young modulus
This equation shows that,
Bending $\delta \propto \frac{l^{3}}{b d^{3} \mathrm{Y}}$
Means for reduce the bending for the given load, the distance between two support must be small or one should use a material of beam with large Young's modulus.
Similar Questions
In nature the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus, the vertical through the centre of gravity does not fall withinthe base. The elastic torque caused because of this bending about the central axis of the tree is given by $\frac{{Y\pi {r^4}}}{{4R}}$ $Y$ is the Young’s modulus, $r$ is the radius of the trunk and $R$ is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.
In nature the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus, the vertical through the centre of gravity does not fall withinthe base. The elastic torque caused because of this bending about the central axis of the tree is given by $\frac{{Y\pi {r^4}}}{{4R}}$ $Y$ is the Young’s modulus, $r$ is the radius of the trunk and $R$ is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.
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