derivation of sagging expression


by sharan swarup
Tags: youngs modulus
sharan swarup
sharan swarup is offline
#1
Mar10-12, 02:30 AM
P: 92
A bar of length l, breadth b, and depth d when loaded at the centre by a load W sags by
an amount given by
δ = W l^3/(4bd^3Y). Here Y is the young's modulus of the wire. My textbook says that we have to use little calculus to derive this expression. Can you please derive this?
Phys.Org News Partner Physics news on Phys.org
Beam on target: CEBAF accelerator achieves 12 GeV commissioning milestone
Modification of structural composite materials to create tailored lenses
High power laser sources at exotic wavelengths
Bill_K
Bill_K is offline
#2
Mar10-12, 05:13 AM
Sci Advisor
Thanks
Bill_K's Avatar
P: 3,846
It gets pretty complicated. But take a look at the Wikipedia article "Euler–Bernoulli beam theory", especially the section "Three-point bending" and see if that is any help.

"The shear is constant in absolute value: it is half the central load, P/2. It changes sign in the middle of the beam. The bending moment varies linearly from one end, where it is 0, and the center where its absolute value is PL/4. The deformation of the beam is described by a polynomial of third degree over a half beam (the other half being symmetrical)."


Register to reply

Related Discussions
derivation of expression for force Classical Physics 3
Landau's derivation of the Langangian expression Classical Physics 4
Sagging Bottom Quantum Box and Pertubation Advanced Physics Homework 1
The sagging effect and angular speed. Introductory Physics Homework 1
Asteroid Collision Course and Sagging Backpack Introductory Physics Homework 6