Bending Moment Diagram for a Beam Loaded with Concentrated Loads at Equal Intervals

A bending moment diagram is a graphical representation of the variation of bending moment along the length of a beam. It helps in understanding the distribution of internal forces and moments within the beam under various loading conditions. In the case of a beam loaded with concentrated loads at equal intervals, the bending moment diagram will have certain characteristics.

1. Horizontal Straight Line at Zero Moment:
At the points where the concentrated loads are applied, the bending moment will be constant and equal to the magnitude of the applied load multiplied by the distance between the loads. These points will result in horizontal straight lines on the bending moment diagram, representing the constant bending moment caused by the concentrated loads.

2. Inclined Straight Line between Concentrated Loads:
Between the points of concentrated loads, the bending moment diagram will have inclined straight lines. The slope of these lines will be determined by the difference in bending moments at the adjacent concentrated loads. The change in bending moment can be calculated by multiplying the difference in applied loads by the distance between them.

3. Parabolic Curve:
The bending moment diagram will have a parabolic shape between the inclined straight lines. This parabolic curve represents the variation of bending moment between the concentrated loads. The maximum bending moment occurs at the midpoint between two adjacent concentrated loads, where the slope of the bending moment curve changes from increasing to decreasing.

The shape of the bending moment diagram depends on the number and magnitude of concentrated loads, as well as the spacing between them. If the loads are equal and spaced at equal intervals, the bending moment diagram will consist of horizontal straight lines at the points of loads, inclined straight lines between the loads, and a parabolic curve in between.

In conclusion, for a beam loaded with concentrated loads at equal intervals, the bending moment diagram will consist of horizontal straight lines at the points of loads, inclined straight lines between the loads, and a parabolic curve in between. These characteristics help engineers analyze the internal forces and moments within the beam and design appropriate structural elements to ensure the beam's safety and stability.