Beam statics is a branch of mechanics that deals with the analysis of forces and moments acting on a beam that is in a state of equilibrium. It is used to determine the internal forces and deformations of a beam under different loading conditions.
The different types of loads in beam statics include point loads, distributed loads, and concentrated moments. Point loads are applied at a specific point along the beam, distributed loads are applied over a certain length of the beam, and concentrated moments are applied at a specific point and cause the beam to rotate.
To calculate the reactions at supports in beam statics, you need to first draw the free body diagram of the beam and apply the equations of equilibrium. The sum of all forces in the vertical direction must equal zero, and the sum of all moments about any point must also equal zero. By solving these equations, you can determine the reactions at the supports.
A statically determinate beam is one in which the reactions at the supports can be determined using only the equations of equilibrium. This means that the number of unknown forces and moments is equal to the number of equations available to solve for them. In contrast, an indeterminate beam requires additional equations, such as compatibility equations, to determine all the unknown forces and moments.
To determine the internal forces and deformations in a beam under a continuous load, you need to use the principles of superposition. This involves breaking down the continuous load into smaller, simpler loads, and calculating the internal forces and deformations for each of these loads separately. The results are then combined to determine the total internal forces and deformations in the beam.
