# Vertical Beam under eccentric Load

• GrassCube
In summary, the conversation discusses a problem involving a vertical hanging cylindrical beam with an eccentric load at the bottom. The load is parallel to the swinging plane and does not create a torsion force. The goal is to find a parametric equation to approximate the maximum deflection of the beam at the bottom. Possible solutions include allowing the beam to rotate until the load lines up with the hinge or taking into account strain in the beam.
GrassCube
Hi,
I've been trying to solve a problem which i don't even know how to approach.

I have a vertical hanging cylindrical beam (free to swing sideways but not around itself), the beam is subjected to an eccentric load, downwards, at the bottom of it. The load is parallel to the swinging plane (it dose not create a torsion force in the beam).

I want to get to a parametric equation that can give me an approximation of the max deflection of the beam at the bottom.

If you have a stiff light vertical beam hinged at the ceiling and with an eccentric vertical load P applied at the other end eccentric to its cg at a horizontal distance e from the cg, I would think the beam will rotate until the line of action of P lines up with the hinge, that is, the beam will swing laterally at the bottom a horizontal distance e from its original position, making an angle with the vertical which depends on its length.

PhantomJay is correct, unless you want to account for strain in the beam as well.

## 1. What is a vertical beam under eccentric load?

A vertical beam under eccentric load refers to a structural element that is subjected to a load that is not directly in line with the center of gravity of the beam. This creates a bending moment on the beam, causing it to deform and potentially fail.

## 2. What factors affect the behavior of a vertical beam under eccentric load?

The behavior of a vertical beam under eccentric load is affected by several factors, including the magnitude and direction of the load, the distance of the load from the center of gravity of the beam, and the properties of the beam such as its material and cross-sectional shape.

## 3. How is the bending moment calculated for a vertical beam under eccentric load?

The bending moment for a vertical beam under eccentric load can be calculated by multiplying the magnitude of the load by the distance from the center of gravity of the beam to the line of action of the load. This is known as the moment arm.

## 4. What are the potential failures that can occur in a vertical beam under eccentric load?

The most common failure modes for a vertical beam under eccentric load are excessive deflection and shear failure. Excessive deflection occurs when the bending moment exceeds the beam's capacity, causing it to deform beyond its acceptable limits. Shear failure occurs when the shear forces on the beam exceed its strength, causing it to fail along a diagonal line.

## 5. How can the design of a vertical beam under eccentric load be optimized?

The design of a vertical beam under eccentric load can be optimized by considering the load magnitude and direction, as well as the properties of the beam. Increasing the beam's cross-sectional area or using a stronger material can help increase its capacity to resist bending moments. Additionally, locating the load as close to the center of gravity of the beam as possible can reduce the bending moment and potential for failure.

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