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20 Oct 2022

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Stress analysis and related calculations are an integral part of civil engineering. Any structure's primary purpose is to transmit forces and loads. Loading is the process of applying force to an item. A multi-story steel-framed structure supports loads like the roof, floors, and exterior walls. These loads are transferred via the steel frame to the building's foundation, where it is supported. In order to understand how applied pressures or loads result in internal stress and related strains in structures, stress analysis is used.

There are various structures we use in construction as well as in the field of mechanical engineering. The commonly used ones are cantilever beams, simply-supported beams and overhanging beams. In the practical scenario, the various loading conditions available are as follows.

UDL (Uniformly Distributed Load): The load will be distributed and applied continuously.

**Common examples of the cantilever beam in real engineering are as follows:**

** **

In the above cases, there is a constant load that is applied in the one due to its own weight and the drag force experienced due to airflow. Similarly, the weight of the crane with hooks and the motor will apply a constant load to the beam. This type of load can be classified under the class of UDL. In particular, the column and beams used for the construction of buildings will have constant loads acting on the beam. That gives the insight to choose UDL:

Now, let’s discuss the governing equations for these beams along with the Shear Force Diagram and the Bending Moment diagram.

The Magnitude of the load applied and the reaction force by the = WX

The equation is developed like this because the load is acting per length so the total loading available in magnitude is w*x load x Displacement

Consider a cantilever beam with a UDL applied to it

The Force can be converted to a point load by multiplying with the length

Load = wm N acting at the center of the Beam

Load at each point = wx

Here the x represents the length of the beam from the free end.

Stress is the internal resistive force that develops when a material is subjected to an external force.

**Stress= Force/ Area**

Stress at each point for UDL = wx/A N/m2

**Stress Analysis** is the process by which engineers assess the load intake in structures to assure structural dependability and offer solutions to various stresses. For instance, a stress analysis during the design of a building might present the computation of the shear force and bending distributions in beams.

**Deflection is the deformation happening to the structure due to loading conditions. The deflection to the beam is proportional to the load and distance as the load is applied throughout the structure.**

Deflection *at each point = *`w/24(-x^4+4L^3x-3L^4 )`

*At x=0 Ymax=*wl"3" /8EI*At x=L Ymax=*0

Ymax represents the displacement that occurred due to loading. The below image shows the same governing equation related to both UDL and Moment applied,

The above image represents the variation of force and bending moment for a cantilever beam when we apply a UDL to it. These governing equations are being coded and are working behind the FEA solver to get the desired result if you click mesh and run in SolidWorks

In case of stress at every point = F/A

As we can see that at each section, the load applied =Wx Load * Distance applied for each distance the load will be calculated and will be marked.

The above is the equation for the Deflection of the beam so the deflection is related to the distance of the applied load the same way the solver will apply each and every length and the corresponding deflection is calculated.

By using all the governing equations we can see the inputs are the Length of the beam, the Magnitude of the load at a point based on these inputs and the stress at each point are calculated and the bending moment at each point in the SolidWorks for better execution.

Author

Navin Baskar

Author

Skill-Lync

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