# A beam: need to calculate its max moment and deflection

• Poke
In summary, the problem is to determine the maximum moment and maximum deflection of a beam with a span of 40 feet and a uniform loading of 500 pound/feet and a point load of 4000 pound at mid span, supported by a roller and a pin. The Force method is to be used, but since it is a Determinate structure, the method may not be applicable. The suggested solution involves adding a virtual force at mid span to generate two virtual moments, and using the equations Delta = integration of m*M / EI and f = integration of m*m / EI to calculate the deflection. Two separate equations for the moments on each side of the center must be written and integrated to account for the discontinuity in
Poke

## Homework Statement

Beam spans 40 feet, with uniform loading of 500 pound/feet and a point load of 4000 pound at mid span.
Support A is roller, support B is pin.
How to determine the maximum moment and maximum deflection due to the loads.
Use Force method

Since it is a Determinate structure, I am not very sure how to use the method.

Delta + f F = 0

find Delta

## The Attempt at a Solution

I suppose I need to add a virtual force of 1 pulling the structure down at mid span... so that it generates 2 virtual moments (m).

From the original structure, I can also get 2 real moments (M).

Then using the equations:

Delta = integration of m*M / EI ...
f = integration of m*m / EI

And then I will know deformation??

#### Attachments

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I guess that's the unit load method for determining deflections. When calculating M and m you need to show it as a function of x.
And since fthe applied and virtual point loads result in a discontinuity In moment, you have to write 2 equations for the moments, one for the left side of center, and one for the right. Then do the integrations and add them all up

## 1. How do I calculate the maximum moment of a beam?

The maximum moment of a beam can be calculated by using the formula M = WL/8, where M is the maximum moment, W is the total load applied to the beam, and L is the length of the beam.

## 2. What factors affect the maximum moment of a beam?

The maximum moment of a beam is affected by the type of load applied (point load or distributed load), the magnitude and distribution of the load, and the length and material of the beam.

## 3. How do I calculate the deflection of a beam?

The deflection of a beam can be calculated using the formula δ = (WL^3)/(48EI), where δ is the deflection, W is the total load applied to the beam, L is the length of the beam, E is the modulus of elasticity of the beam material, and I is the moment of inertia of the beam's cross-sectional area.

## 4. What is the maximum allowable deflection for a beam?

The maximum allowable deflection for a beam depends on the type of beam and its intended use. Generally, for residential construction, the maximum allowable deflection is L/360, where L is the length of the beam. For commercial and industrial buildings, the maximum allowable deflection is typically L/240.

## 5. Can I use the same calculations for all types of beams?

The calculations for maximum moment and deflection may vary depending on the type of beam, such as a simply supported beam, cantilever beam, or continuous beam. It is important to use the appropriate formulas and consider the specific characteristics of the beam in order to accurately calculate its maximum moment and deflection.

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