Bending stress + bending moment

In summary: This can be done by considering the neutral axis of the beam. The maximum bending stress will occur at the furthest point from the neutral axis. By using the given dimensions of the steel strip and the diameter of the drum, you can determine the distance from the neutral axis to the outer surface of the steel strip. Once you have this value, you can plug it into the formula for bending stress and solve for the maximum stress. In summary, to find the maximum stress produced when bending a steel strip around a drum of diameter 4 m, you can use the formula for bending stress and determine the value of 'y' at the furthest point from the neutral axis of the beam. Then, plug this value into the formula and solve for the
  • #1
ar202
45
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Homework Statement



A steel strip of breadth 50 mm and depth 3 mm needs to be bent around a drum of diameter 4 m. What bending moment is required and what will be the maximum stress produced? The modulus of elasticity of the steel is 210 GPa

Homework Equations



[tex]
\frac{M}{I} = \frac{\sigma _b}{y} = \frac{E}{R}
[/tex]

The Attempt at a Solution



I'm able to find the bending moment by finding the second moment of area...

1.05 x1011 x 1.125 x10-10 = 11.8 Nm

however I'm stuck on how to then go on and find the maximum stress
 
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  • #2
ar202 said:

Homework Statement



A steel strip of breadth 50 mm and depth 3 mm needs to be bent around a drum of diameter 4 m. What bending moment is required and what will be the maximum stress produced? The modulus of elasticity of the steel is 210 GPa

Homework Equations



[tex]
\frac{M}{I} = \frac{\sigma _b}{y} = \frac{E}{R}
[/tex]

The Attempt at a Solution



I'm able to find the bending moment by finding the second moment of area...

1.05 x1011 x 1.125 x10-10 = 11.8 Nm

however I'm stuck on how to then go on and find the maximum stress
You have already noted the formula that bending stress = My/I...you just need to identify the value for 'y' where the bending stress is at its maximum.
 

What is bending stress?

Bending stress is a type of stress that occurs in a structural element when it is subjected to a bending load. It is caused by the internal forces that act on the element as a result of the applied load.

What is bending moment?

Bending moment is a measure of the internal bending forces acting on a structural element. It is the product of the applied load and the distance from the point of application of the load to the point of interest on the element.

How is bending stress calculated?

Bending stress is calculated by dividing the bending moment by the section modulus of the structural element. The section modulus is a measure of the resistance of the element to bending.

What are the factors that affect bending stress?

The factors that affect bending stress include the magnitude and location of the applied load, the material properties of the structural element, and the cross-sectional shape and size of the element.

What are the applications of bending stress and bending moment in engineering?

Bending stress and bending moment are important considerations in the design of structural elements such as beams, columns, and bridges. They are also used in the analysis of mechanical components, such as shafts and gears, to ensure they can withstand the applied loads without failure.

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