# How Do You Calculate Incremental Axial Stress in a Preloaded Elastic Beam?

• will4
In summary, the conversation discusses the calculation of an increment in axial stress in an elastic rectangular beam that is fixed from both ends and under a certain tensile load. The dimensions of the beam, elastic modulus, initial axial load, and deflection in the center are given. The question is how to determine the load on the top fiber when the bottom fibers have no axial stress and the whole beam is in compression. The conversation also mentions the use of preloading in concrete beams to prevent any part of the beam from being in tension under a transverse load.
will4
Seems that most of the textbooks are dealing with elastic beam calculations, where a beam is fixed from both ends and initially there is no axial stress or load applied.

My problem is different in a way that an elastic rectangular beam is fixed from both ends and it is under certain tensile load F (given). I know the bending deflection y in the center of the beam due to applied load in transverse direction (that load is not given).

The question is how to calculate an increment in axial stress by knowing the deflection y in the center of the beam that is generated by applying a load in transverse direction?

Given:
Dimension of the beam, L, h, w
Elastic modulus (both tensile and bending)
Deflection in the center, y

Any help appreciated.

Last edited:
If I recall correctly;
a) For a beam not under a preload, the top is in compression and the bottom in tension, and the middle fiber has no axial stress, when the beam is loaded tranversally.
b) Now apply a compressive force to both ends so that the bottom fibers have no axial stress, and the whole beam is in compression.

What would be the load on the top fiber? Would it be the compressive stress in a) plus that added in part b) .

As a side note, concrete beams are often preloaded in compression so that no part of the beam beam will ever (never) be in tension under a transverse load.

Hope that gets you started.

## 1. What is the unusual elastic beam problem?

The unusual elastic beam problem is a theoretical physics problem that involves determining the shape of an elastic beam when it is under different forms of external stress. This problem is often used as an exercise in advanced mechanics and is also relevant to structural engineering and material science.

## 2. What makes this problem unusual compared to other beam problems?

The unusual aspect of this problem is that it involves a combination of different types of stress, such as bending, twisting, and axial forces, which are typically considered separately in traditional beam problems. This makes the problem more complex and challenging to solve.

## 3. What are some practical applications of the unusual elastic beam problem?

The unusual elastic beam problem has practical applications in the design and analysis of structures and materials that are subject to multiple types of stress, such as aircraft wings, bridges, and mechanical components. It can also help engineers and scientists understand the behavior of elastic materials under different types of stress.

## 4. What are the key factors that determine the shape of the elastic beam in this problem?

The shape of the elastic beam is determined by several factors, including the type and magnitude of external stress, the material properties of the beam, and the boundary conditions at each end of the beam. These factors interact with each other and must be carefully considered in order to accurately solve the problem.

## 5. Are there any real-world examples of the unusual elastic beam problem?

Yes, there are many real-world examples of the unusual elastic beam problem. One notable example is the design of suspension bridges, where the beams are subject to various forms of stress, such as bending and twisting, from the weight of the bridge and the movement of vehicles. Another example is the design of airplane wings, which must withstand different types of stress from aerodynamic forces and the weight of the aircraft.

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