Deflection at any point in fixed beam

In summary, deflection at any point in a fixed beam refers to the amount of bending or displacement that occurs at a specific location on the beam when a load is applied. This is a crucial factor to consider in structural engineering as excessive deflection can lead to structural failure. It is influenced by various factors such as the type and magnitude of the load, the length and stiffness of the beam, and the material properties. Engineers use mathematical equations and structural analysis techniques to calculate and predict deflection in order to design safe and stable structures.
  • #1
sunil.hk1
1
0
give formula or reference for finding deflection at any point in beam (fixed at both ends) due to couple acting intermediate in the beam? its urgent...
 
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  • #2
sunil.hk1 said:
give formula or reference for finding deflection at any point in beam (fixed at both ends) due to couple acting intermediate in the beam? its urgent...

I'd start with Roark's Formulas for Stress and Strain.

CS
 
  • #3
I think the easiest thing is to define the loading using singularity functions, set it equal to EIy'''' (where E = elastic mod, I = moment of inertia, y'''' = fourth derivative of deflection); then successively integrate to get the shear force, moment, and finally the deflection as a function of x (the position along the beam). and determining the integration constants from the boundary conditions (such as at x = 0 and x = l, y = 0).

example of the singularity functions
http://www.roymech.co.uk/Useful_Tables/Beams/Singularity.html

(this is assuming small deflections by the way)
 
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What is deflection at any point in a fixed beam?

Deflection at any point in a fixed beam refers to the vertical displacement of a specific point on the beam as a result of applied loads. It is a measure of the flexibility and stiffness of the beam.

How is deflection at any point in a fixed beam calculated?

Deflection at any point in a fixed beam can be calculated using the Euler-Bernoulli beam theory, which takes into account the beam's material properties, cross-sectional area, and applied loads. It can also be calculated using numerical methods such as the finite element method.

What factors affect deflection at any point in a fixed beam?

The amount of deflection at any point in a fixed beam is affected by several factors. These include the magnitude and location of applied loads, the beam's length and cross-sectional area, and the material properties of the beam.

How does deflection at any point in a fixed beam impact the beam's strength?

Deflection at any point in a fixed beam can impact the beam's strength by causing it to bend and potentially fail under excessive loads. It is important to consider the maximum allowable deflection when designing a fixed beam to ensure it can withstand the expected loads.

Can deflection at any point in a fixed beam be reduced?

Deflection at any point in a fixed beam can be reduced by increasing the beam's stiffness through design modifications, such as changing the material or cross-sectional area. It can also be reduced by adding additional supports or increasing the beam's thickness.

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