Ratio of load carrying capacity of a fixed beam to that of a simply supported beam having same maximum bending moment under UDL throughout the span:

To understand the ratio of load carrying capacity between a fixed beam and a simply supported beam, let's first discuss the characteristics of each type of beam.


- A fixed beam is a beam that is supported at both ends and is rigidly connected to its supports.
- The fixed beam is capable of resisting both vertical and horizontal forces.
- It experiences maximum bending moment at the supports and zero bending moment at the midpoint of the span.
- The fixed beam has higher stiffness compared to a simply supported beam.


- A simply supported beam is a beam that is supported at both ends but not rigidly connected to its supports.
- The simply supported beam is capable of resisting vertical forces only.
- It experiences maximum bending moment at the midpoint of the span and zero bending moment at the supports.
- The simply supported beam has lower stiffness compared to a fixed beam.


The load carrying capacity of a beam is determined by its ability to resist bending moments. The bending moment in a beam is directly proportional to its load carrying capacity. Therefore, the ratio of load carrying capacity between a fixed beam and a simply supported beam can be determined by comparing their bending moments.


Assuming both the fixed beam and simply supported beam have the same maximum bending moment under a uniform distributed load (UDL) throughout the span, we can compare their load carrying capacities.


Let's denote the load carrying capacity of the fixed beam as C_fixed and the load carrying capacity of the simply supported beam as C_simply.

Since the maximum bending moment is the same for both beams, we can write:

C_fixed / C_simply = M_fixed / M_simply

Where M_fixed is the maximum bending moment for the fixed beam and M_simply is the maximum bending moment for the simply supported beam.

Since both beams have the same maximum bending moment, the ratio simplifies to:

C_fixed / C_simply = 1

Therefore, the ratio of load carrying capacity between a fixed beam and a simply supported beam having the same maximum bending moment under a UDL throughout the span is 1.

In conclusion, the load carrying capacity of a fixed beam is equal to that of a simply supported beam when they have the same maximum bending moment under a UDL throughout the span. However, it is important to note that a fixed beam is generally stiffer and can resist larger loads compared to a simply supported beam due to its rigid connections.

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