This sheet calculates the maximum displacement and stress for a simply supported beam. A simply supported beam is vertically supported at each end with each end free to rotate. Two loading cases are considered, a distributed load over the length of the beam and a concentrated load at the center of the beam. The loading case can be chosen using the first table below.
First, the length of the beam is defined:
Next, choose the loading condition. The choice of row in the table sets the equations used for the maximum displacement and the maximum bending moment. The load can be adjusted by editing the relevant table cell.
The material can be chosen using the following table:
Aluminum Alloys
Steel, Alloys
Finally, the cross-section of the beam can be chosen from the following table. The dimensions of the section can be adjusted using the relevant cells in the table below. The figure above the table updates as the rows are changed to indicate the meaning of the various dimensions.
The maximum displacement can now be calculated. The maximum displacement occurs at middle of beam.
=-7.53138075313808mm
Finally, the beam bending stress equation can be used to calculated the maximum stress. The maximum stress will be a tensile stress at the bottom of the beam and an equal magnitude compressive stress at the top of the beam for the symmetric sections used here. Like the maximum displacement, the maximum stress occurs at the middle of the beam.
