Finding the maximum load of a bar from the yield stress

In summary, we have a bar with dimensions of 500mm x 10mm x 3mm and a load of 30n applied at the center. The maximum yield stress is 150 MPa. To calculate the maximum load the bar can take, we can use the equation stress = M*y/I and rearrange for M. For a simply supported beam, the maximum bending moment occurs at the center and is given by Mmax = PL/4 where P is the applied load and L is the length of the beam. Therefore, we can use this equation to find the maximum load from the yield stress.
  • #1
Lap9387
7
0

Homework Statement


I have a bar, 500mm long (0.05m) 10mm wide (0.01m) and 3mm deep (0.003 m)

The bat has a load applied in the centre of 30n

I know the maximum yield stress is 150 mpa 150x10^6

How do I calculate the maximum load the bar can take?


Homework Equations



I used stress = m y / I



The Attempt at a Solution



I calculated the bending moment to be 3.75 at 250mm (.25m) using a shear bending diagram,

I then reversed the equation above to get:

150x10^6 = 0.0015m/2.25x10^-11

Which gives m as : (150x10^6 x 2.25x10^-11) / 0.0015

M = 2.25

I know the bending moment is at .25 m

So divide 2.25 / .25

I get 9


The answer can't be 9n as the question uses 30n

Can someone please show me how to solve this?.

Thanks in advance x
 
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  • #2
How is the bar supported? Are the two ends simply supported or fixed, etc?

The type of supports affect the maximum bending moment, which will affect your maximum load.
 
  • #3
Sorry, the bar is simply supported at either end
 
  • #4
For a simply supported beam, the maximum bending moment occurs at the center and is given by

Mmax =PL/4 where P= applied load and L= length of beam
 
  • #5
So I can then use this to find the max load from the yield stress??
If so, how?
 
  • #6
Lap9387 said:
So I can then use this to find the max load from the yield stress??
If so, how?


Use your first equation and rearrange for M.

σ = My/I
 
  • #7
thank you for this...
 

1. What is the yield stress of a material?

The yield stress of a material is the amount of stress or force that a material can withstand before it permanently deforms or breaks. It is an important factor in determining the strength and stability of a material.

2. How do you find the maximum load of a bar from the yield stress?

The maximum load of a bar can be found by multiplying the yield stress of the material by the cross-sectional area of the bar. This is known as the yield strength and is typically measured in units of force per unit area, such as pounds per square inch (psi) or megapascals (MPa).

3. What factors can affect the yield stress of a material?

The yield stress of a material can be affected by various factors such as the type of material, its composition and microstructure, temperature, and the presence of impurities or defects. In addition, the manufacturing process and any external forces or stresses applied to the material can also impact its yield stress.

4. How is the yield stress determined in a laboratory setting?

In a laboratory setting, the yield stress of a material is typically determined through a tensile test. This involves applying a gradually increasing force to a sample of the material until it reaches its yield point, where it begins to deform. The yield stress is then calculated by dividing the force at the yield point by the original cross-sectional area of the sample.

5. Why is it important to know the maximum load of a bar from the yield stress?

Knowing the maximum load of a bar from the yield stress is important for designing and engineering structures and components that can withstand the expected forces and stresses they will encounter. It also helps ensure the safety and reliability of these structures by preventing them from exceeding their yield strength and potentially failing.

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