# Calculate the reduction in the deflection at the free end

• Sonic Tseh
In summary, the conversation discusses solving the deflection for a cantilever beam with a cable support arrangement. The speaker suggests approximating the distributed load as two equal point loads and treating the system as a truss to solve for the deflection at the cable supported end using joint deflection methods. The speaker acknowledges that this may not be the most accurate method without a computer program or hand calculation.
Sonic Tseh
Homework Statement
If a s275 533x210x82UB cantilever beam is 3m and it's free end is held up by a s275 35mm diameter steel tie member inclined at 45 degree to the horizontal and attached to the vertical column, calculate the reduction in the deflection at the free end of the beam compared with the cantilever support arrangement before and after. A designed UDL is 70.58kN/m on it.
Relevant Equations
Under Hooke's Law
I can solve the deflection if only cantilever beam by deflection formula, but i have no idea for this question if calculated with a cable support arrangement.

I am not sure of an exact solution, but I would approximate it by treating the distributed load as 2 equal point loads with a value of one half the total distributed load applied at each end of the beam, and by considering the fixed end as a pinned end. Then you can treat the system as a truss and solve for the deflection at the cable supported end by using truss joint deflection methods. That is probably not the best way to do it, but it is the way I would do it, in absence of a tedious hand calc or computer program ( if you trust it).

## 1. What is meant by "reduction in deflection"?

The reduction in deflection refers to the decrease in the amount of bending or deformation that occurs at the free end of a structure or material. It is typically measured in units of length, such as millimeters or inches.

## 2. How is the reduction in deflection calculated?

The reduction in deflection can be calculated by comparing the initial deflection at the free end to the final deflection after a force or load has been applied. The difference between the two values is the reduction in deflection.

## 3. What factors can affect the reduction in deflection?

The reduction in deflection can be influenced by various factors, including the material properties of the structure, the magnitude and direction of the applied force, the geometry and shape of the structure, and the support conditions at the free end.

## 4. Why is calculating the reduction in deflection important?

Calculating the reduction in deflection is important because it allows engineers and scientists to assess the structural integrity and stability of a material or structure under different loading conditions. It can also help determine the maximum load that a structure can withstand before experiencing excessive deflection or failure.

## 5. How can the reduction in deflection be used in practical applications?

The reduction in deflection can be used in practical applications to design and optimize structures, such as bridges, buildings, and aircraft, to ensure they can withstand expected loads without excessive deflection. It can also be used to evaluate the performance of materials and to identify potential failure points in a structure.

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