How Do Permissible Loads Relate to Bending and Shear Stresses?

• t_n_p
In summary, the conversation discusses a problem involving calculating the permissible load for a T beam. The individual is seeking equations to relate the permissible load to tension, compression, and shear stress. It is advised to calculate the neutral axis and moment of inertia of the T beam and determine which stress controls the maximum bending moment in order to solve for the permissible load. The individual is also asked to show their attempt at calculating some of these values.
t_n_p

Homework Statement

http://img150.imageshack.us/img150/756/17311663go9.jpg

The Attempt at a Solution

I wasn't 100% sure whether this should be here or in the Engineering section, hopefully I've got it right. Anyway, I'm fairly unfamiliar with this type of problem and basically I'm just looking for an equation that will relate the permissible load to the tension and compression (part a) and an equation relating this permissible load to shear stress (part b). I've had a look through my notes and found nothing thus far.

Thanks to anyone who can help!

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This belongs in the engineering section, but anyway, you first have to calculate the neutral axis and moment of inertia of the T beam. Then see which stress (compression or tension) controls the max bending moment, and back solve for P based on that moment. Please show your attempt at calculating some of these values.

I can provide some information and equations that may help with this problem. Bending stress is the stress that occurs when a force is applied to an object causing it to bend or deform. This is usually calculated using the equation σ = My/I, where σ is the bending stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia.

Shear stress, on the other hand, is the stress that occurs when a force is applied parallel to an object's cross-sectional area, causing it to shear or slide. This is usually calculated using the equation τ = VQ/Ib, where τ is the shear stress, V is the shear force, Q is the first moment of area, I is the moment of inertia, and b is the width of the object.

For part a, to relate the permissible load to the tension and compression, we can use the equation σ = P/A, where P is the load, A is the cross-sectional area, and σ is the stress. This equation assumes that the object is under uniform stress.

For part b, to relate the permissible load to the shear stress, we can use the equation τ = P/A, where P is the load, A is the cross-sectional area, and τ is the shear stress. This equation also assumes uniform stress.

I hope this helps with your problem and provides a starting point for finding the correct equations for your specific situation. It is always important to carefully consider all the variables and assumptions when using equations to solve engineering problems. Good luck!

1. What is the difference between bending and shear stresses?

Bending stress is the stress that occurs in a beam or structure when a bending moment is applied, causing the beam to bend. Shear stress, on the other hand, is the stress that occurs when two forces act in opposite directions parallel to the surface of an object, causing it to slide or shear.

2. How are bending and shear stresses calculated?

Bending stress is calculated using the formula σ = My/I, where σ is the bending stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. Shear stress is calculated using the formula τ = VQ/It, where τ is the shear stress, V is the shear force, Q is the first moment of area, I is the moment of inertia, and t is the thickness of the object.

3. What are the factors that affect bending and shear stresses?

The factors that affect bending stress include the magnitude of the bending moment, the shape and size of the beam or structure, and the material properties such as the modulus of elasticity. The factors that affect shear stress include the magnitude of the shear force, the shape and size of the object, and the material properties such as the shear modulus.

4. What are some common applications of bending and shear stresses?

Bending stress is commonly seen in structures such as bridges, buildings, and beams. Shear stress is commonly seen in structures such as columns, bolts, and rivets. Both bending and shear stresses also play important roles in the design and analysis of various mechanical components such as gears, shafts, and bearings.

5. How can bending and shear stresses be reduced or controlled?

Bending and shear stresses can be reduced or controlled by using stronger or stiffer materials, increasing the size or shape of the object, or by adding reinforcements such as beams or columns. Additionally, proper design and analysis techniques can also help to minimize bending and shear stresses in structures and mechanical components.

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