$**$Analysis of a Two$-$Span Beam with Concentrated Loads$**$

In civil engineering, the analysis of a two$-$span beam with concentrated loads involves determining the reactions, shear forces, and bending moments at various points along the beam. This type of beam typically consists of two supported spans with concentrated loads applied at specific locations.

The analysis begins by calculating the reactions at the supports using the equations of equilibrium. Once the reactions are known, shear force and bending moment diagrams can be constructed to illustrate the internal forces acting on the beam. The shear force diagram shows the variation of vertical forces along the length of the beam, while the bending moment diagram illustrates the variation of moments.

The concentrated loads applied to the beam can cause discontinuities in the shear force and bending moment diagrams, indicating sudden changes in the internal forces. These discontinuities occur at the points where the concentrated loads are applied and are typically represented by vertical jumps in the diagrams.

Engineers use the analysis of a two$-$span beam with concentrated loads to ensure that the beam can safely support the applied loads without exceeding its capacity or experiencing excessive deflection.

$**$Objective Type Question:$**$

In the analysis of a two$-$span beam with concentrated loads, what do discontinuities in the shear force and bending moment diagrams indicate?

A$)$ Uniformly distributed loads

B$)$ Changes in beam material properties

C$)$ Applied concentrated loads

D$)$ Variations in support reactions

Choose the correct option and provide a brief explanation of your choice.