Can Bending Stress on Curved Beams Be Calculated Using a Simple Formula?

In summary: These courses are taken by students who have already had a course on elementary strength of materials, which is where the formula Mc/I comes from.Curved beams are not as common as straight beams in engineering applications, but there are some important exceptions. In particular, the design of bridges and the design of tunnels often involve curved beams.In summary, the conversation discusses a problem involving a curved member of circular cross section that is bent in the shape of a half circle and fixed at the base. The person is trying to find the bending stress at the base and is wondering if they can use the formula Mc/I, but is unsure of what to use for the area moment of inertia. Curved beams cannot be treated the same as straight beams and are
  • #1
gomerpyle
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I have a problem where I'm considering a curved member of circular cross section bent in the shape of a half circle and fixed at the base. A force is applied perpendicular to it (so in the picture, the dot is the force going 'into' the screen at the top view) and I'm trying to find the bending stress at the base. Can I approach this as a simple Mc/I situation with c being half the diameter of the rod, and M being the distance of F to the base? I'm confused, though, on what I would use for the area moment of Inertia.

Any assistance would be appreciated. Thank you.
 

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  • #2
gomerpyle said:
I have a problem where I'm considering a curved member of circular cross section bent in the shape of a half circle and fixed at the base. A force is applied perpendicular to it (so in the picture, the dot is the force going 'into' the screen at the top view) and I'm trying to find the bending stress at the base. Can I approach this as a simple Mc/I situation with c being half the diameter of the rod, and M being the distance of F to the base? I'm confused, though, on what I would use for the area moment of Inertia.

Any assistance would be appreciated. Thank you.
You can't treat the bending of curved beams in the same manner as you do the bending of straight, prismatic beams.

The bending of curved beams is usually treated in courses on advanced strength of materials.
 

Related to Can Bending Stress on Curved Beams Be Calculated Using a Simple Formula?

What is bending stress on handle?

Bending stress on handle refers to the amount of force exerted on a handle when it is subjected to a bending load. This stress can cause the handle to bend or deform, and can potentially lead to failure if the stress exceeds the handle's strength.

What causes bending stress on handle?

Bending stress on handle is primarily caused by the application of an external load or force on the handle. This load can be due to the weight of an object being held by the handle, or from the movement or manipulation of the handle itself.

How is bending stress on handle calculated?

Bending stress on handle can be calculated using the formula: σ = Mc/I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis (center) of the handle to the outermost fibers, and I is the moment of inertia of the handle's cross-sectional area.

What factors can affect bending stress on handle?

There are several factors that can affect bending stress on handle, including the material and shape of the handle, the magnitude and direction of the applied load, and the support and constraints of the handle. Other factors such as temperature, corrosion, and fatigue can also play a role.

How can bending stress on handle be reduced or prevented?

To reduce or prevent bending stress on handle, the handle can be designed and manufactured with materials and shapes that can withstand high loads and stress. Proper installation, maintenance, and use of the handle can also help prevent excessive bending stress. Additionally, distributing the load evenly and avoiding sudden or jerky movements can also help reduce bending stress on handle.

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