Simple supported round shaft deflection

In summary, Frank is looking for the deflections of a 1.938" dia. steel shaft at different lengths, supported in bearings at both ends. The shaft has a distributed load of 150lbs. per foot of length, with all of the weight in the center of the rod. Specifically, Frank is looking for deflections of 300 lbs. for 24", 450 for 36", and 600 for 48". To calculate the deflection for a simply supported beam, the formula δ = 5wL^{4}/(384EI) can be used, where L is the distance between supports in inches, w is the distributed load in pounds / inch, E is the Young's modulus for the shaft
  • #1
AQUAPOP
4
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Hello.
I'm looking for the deflections of a 1.938" dia. steel shaft at different lengths.
Supported in bearings at both ends.
150lbs. per foot of length, with all of the weight in the center of the rod.
I.E. how much does the rod deflect of there is 450lbs. pushing down between 36"...
I'm looking for 300 lbs. for 24", 450 for 36", and 600 for 48".

Thanks in advance,
Frank
 
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  • #2
AQUAPOP said:
Hello.
I'm looking for the deflections of a 1.938" dia. steel shaft at different lengths.
Supported in bearings at both ends.
150lbs. per foot of length, with all of the weight in the center of the rod.
I.E. how much does the rod deflect of there is 450lbs. pushing down between 36"...
I'm looking for 300 lbs. for 24", 450 for 36", and 600 for 48".

Thanks in advance,
Frank

For a simply supported beam, the max deflection for an evenly distributed load is

δ = 5wL[itex]^{4}[/itex]/(384EI)

where:
L - distance between supports, in inches
w - distributed load, in pounds / inch
E - Young's modulus for the shaft material
(for example, for steel, E = 29*10[itex]^{6}[/itex] lbs/in[itex]^{2}[/itex])
I - second moment of area for the shaft, in inches[itex]^{4}[/itex]

I for a circular shaft is πD[itex]^{4}[/itex]/64, D - diameter in inches
δ - shaft deflection, in inches
π - constant = 3.14159

Make sure you use the correct units and you are good to go.
 
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1. What is "simple supported round shaft deflection"?

"Simple supported round shaft deflection" refers to the degree of bending or displacement of a round shaft that is supported on both ends and subjected to a load in the middle. This is a common concept in mechanical and structural engineering, and is important in determining the strength and stability of a structure.

2. How is simple supported round shaft deflection calculated?

There are several equations and methods used to calculate the deflection of a simple supported round shaft, depending on the type of load and material properties. One common method is using the Euler-Bernoulli beam theory, which takes into account the length, diameter, and material of the shaft, as well as the applied load. There are also online calculators and software programs available for determining deflection.

3. What factors affect simple supported round shaft deflection?

The amount of deflection in a simple supported round shaft is affected by various factors, including the load magnitude, the type of load (e.g. point load or distributed load), the material properties of the shaft (such as stiffness and Young's modulus), and the length and diameter of the shaft. Other factors that may play a role include temperature, moisture, and any external forces acting on the shaft.

4. Why is simple supported round shaft deflection important?

Understanding and accurately calculating the deflection of a simple supported round shaft is crucial in ensuring the structural integrity and safety of a building or mechanical system. Excessive deflection can lead to structural failure or malfunction, which can have serious consequences. It is also important for engineers to consider deflection when designing and selecting materials for a project.

5. How can simple supported round shaft deflection be reduced or controlled?

There are several methods for reducing or controlling deflection in a simple supported round shaft. These include increasing the diameter or stiffness of the shaft, using stronger materials, adding supports or braces along the length of the shaft, and reducing the applied load. In some cases, a combination of these methods may be necessary to achieve the desired level of deflection.

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