# Writing shear and moment equations for a simple beam problem?

• rtrux4
In summary, the problem involves analyzing a simple beam with a length of 20ft and a distance to reaction of 12ft. The distributed load is 273.33 lb/ft. The equations used are V=r1-w(L-0)+r2=0, M=r1*L-w/2*(L-0)^2+r2*(L-B)=0, r1:=1/B*[w/2*(L-0)^2-w*(L-0)*(L-B)], and r2:=w*(L-0)-r1. After solving for V and M, the values are 2066.67 lb and 12320 lb-ft, respectively. There may be some issues with the units,
rtrux4

## Homework Statement

Analyze a simple beam writing out the integrals in mathcad.

Length: 20ft (L)
Distance to Reaction: 12ft (B)

## Homework Equations

V=r1-w(L-0)+r2=0
M=r1*L-w/2*(L-0)^2+r2*(L-B)=0
r1:=1/B*[w/2*(L-0)^2-w*(L-0)*(L-B)]
r2:=w*(L-0)-r1

## The Attempt at a Solution

I having issues with units or something. But would also like to know if I am on the right track.

V=r1-w(L-0)+r2=0r1:=1/B*[w/2*(L-0)^2-w*(L-0)*(L-B)]r2:=w*(L-0)-r1V=1/12*[273.33/2*20^2-273.33*20*(20-12)]-273.33*20+273.33*20-1/12*[273.33/2*20^2-273.33*20*(20-12)]V=2066.67 lbM=r1*L-w/2*(L-0)^2+r2*(L-B)=0M=1/12*[273.33/2*20^2-273.33*20*(20-12)]*20-273.33/2*20^2+273.33*20-1/12*[273.33/2*20^2-273.33*20*(20-12)]*(20-12)M=12320 lb-ft

## 1. What is a simple beam problem?

A simple beam problem is a common type of problem in structural engineering where a beam is subjected to various loads and the goal is to determine the shear and moment at different points along the beam.

## 2. Why do we need to write shear and moment equations for a simple beam problem?

Shear and moment equations are necessary for analyzing the structural integrity of a beam. They help determine the internal forces and stresses acting on the beam, which are crucial in designing safe and efficient structures.

## 3. How do we determine the shear and moment equations for a simple beam problem?

The shear and moment equations for a simple beam problem can be determined using the equilibrium equations and the properties of the beam, such as its length, support conditions, and applied loads. These equations can also be derived from the bending moment and shear force diagrams.

## 4. What are the common assumptions made when writing shear and moment equations for a simple beam problem?

The common assumptions made include: a) the beam is loaded in the plane of its length, b) the beam is straight and has a constant cross-section, c) the material is homogenous and isotropic, and d) the beam is supported at its ends or at specific points along its length.

## 5. Can shear and moment equations be used for complex beam problems?

Shear and moment equations can be used for more complex beam problems, but additional factors such as beam deformations, material properties, and support conditions may need to be considered. In some cases, more advanced methods such as finite element analysis may be necessary to accurately determine the shear and moment in complex beams.

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