Mechanics of materials ques / stresses in beams

In summary, bending stress and shear stress in beams are two types of stress caused by different types of forces. Bending stress affects the top and bottom surfaces of a beam, while shear stress affects the sides. The maximum bending stress in a beam can be calculated using the formula σ = My/I, where M is the moment applied to the beam, y is the distance from the neutral axis, and I is the moment of inertia. The neutral axis in a beam is an imaginary line that divides the cross-section into a compression zone and a tension zone. The material of a beam affects its strength and different materials have different properties that can affect their ability to resist deformation and failure. Finally, normal stress and shear stress in beams are caused by different
  • #1
macbarbicus
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Homework Statement


refer to attachment


Homework Equations





The Attempt at a Solution


I am completely confused at where to start can someone get me going in the right direction here as to one of the answers.
 

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  • #2
Hi, Macbarbicus, welcome to PF!

Per forum rules, you are going to have list what you believe are the relevant equations, and show some attempt at your work, before we can be of assistance. You should be familiar with the shear flow formula which indicates how the shear stresses vary over the beam cross section.
 
  • #3


I would suggest starting by reviewing the fundamental principles of mechanics of materials, specifically the concepts of stress and strain. In beams, stress is the force per unit area that is exerted on the material and strain is the resulting deformation of the material. The relationship between stress and strain is described by Hooke's Law, which states that stress is directly proportional to strain within the elastic limit of the material.

To solve for stresses in beams, you will need to consider the different types of loads that the beam is subjected to, such as bending, shear, and axial loads. Each type of load will result in a different type of stress on the beam. For example, bending loads will result in tensile and compressive stresses on opposite sides of the beam, while shear loads will result in shear stresses parallel to the cross-section of the beam.

To determine the stresses in a beam, you will also need to know the properties of the material, such as its modulus of elasticity and its moment of inertia. These properties can be found in materials tables or can be calculated using the dimensions and material properties.

Once you have a good understanding of the basic principles and equations involved in calculating stresses in beams, you can then apply them to the specific problem presented in the attachment. Start by identifying the type of loads acting on the beam and then use the appropriate equations to calculate the corresponding stresses. Remember to check your answers and make sure they fall within the elastic limit of the material.

I hope this helps get you started in the right direction. It is always important to have a solid understanding of the fundamentals before attempting to solve more complex problems in mechanics of materials. Good luck!
 

1. What is the difference between bending stress and shear stress in beams?

Bending stress in beams is caused by a force applied perpendicular to the axis of the beam, resulting in a bending or flexural deformation. Shear stress, on the other hand, is caused by a force applied parallel to the cross-sectional area of the beam, resulting in a shearing or sliding deformation. In simple terms, bending stress affects the top and bottom surfaces of a beam, while shear stress affects the sides of a beam.

2. How do I calculate the maximum bending stress in a beam?

The maximum bending stress in a beam can be calculated using the formula σ = My/I, where σ is the bending stress, M is the moment applied to the beam, y is the distance from the neutral axis to the point of interest, and I is the moment of inertia of the cross-sectional area of the beam.

3. What is the neutral axis in a beam?

The neutral axis in a beam is an imaginary line along the cross-section of the beam where there is no stress or deformation when a bending moment is applied. It divides the cross-section into a compression zone and a tension zone, with the compression zone being above the neutral axis and the tension zone below it.

4. How does the material of a beam affect its strength?

The material of a beam plays a significant role in its strength and ability to withstand bending and shear stresses. Different materials have different properties such as yield strength, modulus of elasticity, and ductility, which affect their ability to resist deformation and failure under load. Generally, materials with higher strength and stiffness, such as steel, are better suited for beams compared to weaker materials like wood.

5. What is the difference between normal stress and shear stress in beams?

Normal stress in beams is caused by axial forces or tension/compression loads, resulting in a change in the length of the beam. Shear stress, as mentioned earlier, is caused by lateral forces or loads applied parallel to the cross-section of the beam. Both types of stress can lead to failure in beams, but they affect the beam in different ways and require different calculations for analysis.

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