B How to understand formula for bending of a rectangular rod?

AI Thread Summary
The discussion centers on calculating Young's modulus for a rod experiencing bending under forces. It emphasizes that deflection is linear with force, allowing for the use of superposition when deflections are small. The main inquiry is whether to use just the additional force and the change in deflection or to account for both forces and the total deflection. Clarification is sought on whether the forces are applied at the same location, which could impact the calculations. Understanding the relationship between the forces and deflection is crucial for accurate modulus determination.
Lotto
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TL;DR Summary
If we have a rod shown on the picture below, we can calculate Young's modulus as ##E =\frac{F l^3}{4yab^3}##, where ##a## is a width and ##b## is a height of the rod.

Now my question is: If the rod is already bended with a certain ##y## as on the picture and if we apply an another additional force ##F'## and the total bend would be ##y'##, can we use in the formula to calculate ##E## only ##F'## and ##y'-y##? Or do we have to use ##F+F'## and ##y'##?
The picture:
picture.png
 
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Notice that the deflection is linear with force.
Each force causes a proportional deflection.
So long as the deflection is small, the order of application is not critical.
 
Lotto said:
TL;DR Summary: If we have a rod shown on the picture below, we can calculate Young's modulus as ##E =\frac{F l^3}{4yab^3}##, where ##a## is a width and ##b## is a height of the rod.

Now my question is: If the rod is already bended with a certain ##y## as on the picture and if we apply an another additional force ##F'## and the total bend would be ##y'##, can we use in the formula to calculate ##E## only ##F'## and ##y'-y##? Or do we have to use ##F+F'## and ##y'##?

The picture:
View attachment 358226
You can use superposition if the deflections are not too large.
 
You can reson this one out. Suppose that there is not load, i.e. both ##F## and ##F'## are zero. What does the rod look like? Now add ##F## and ##F'##. How would you calculate the height? You may or may not have to ignore the bending of the rod under its weight.
 
Lotto said:
Now my question is: If the rod is already bended with a certain ##y## as on the picture and if we apply an another additional force ##F'## and the total bend would be ##y'##, can we use in the formula to calculate ##E## only ##F'## and ##y'-y##? Or do we have to use ##F+F'## and ##y'##?
Quick question- are F and F' applied at the same location?
 
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