Stress Function in a Statically Determinate Structure

In a statically determinate structure, the stress function represents the variation of stresses in the structure due to the application of external loads. The influence line for the stress function shows the effect of a unit load moving along the structure on the stress at different points.

Types of Influence Lines

There are several types of influence lines, including linear, parabolic, bilinear, and uniformly rectangular. Each type represents a specific variation of the stress function in the structure.

Explanation of the Correct Answer

The correct answer to the given question is option 'C', which states that the variation of influence line for the stress function in a statically determinate structure is linear.

Reasoning

The variation of the influence line for the stress function is linear because in a statically determinate structure, the stress is directly proportional to the applied load. As the load moves along the structure, the stress at different points also changes linearly.

Example

For example, consider a simply supported beam subjected to a concentrated load at a distance 'x' from one support. The influence line for the stress function at any point on the beam will be a straight line, with the maximum stress occurring directly under the load and decreasing linearly towards the supports.

Advantages of Linear Influence Lines

Linear influence lines have some advantages in structural analysis. They are easier to construct and interpret compared to other types of influence lines. Additionally, linear influence lines provide a good approximation of the actual stress distribution in many practical cases.

Conclusion

In conclusion, the variation of influence line for the stress function in a statically determinate structure is linear. This means that the stress at different points in the structure changes linearly as a unit load moves along the structure. Linear influence lines are commonly used in structural analysis due to their simplicity and good approximation of stress distribution.