A continuous beam ABC is loaded with a concentrated moment at B. End r...
Reaction at End C of a Continuous Beam with Fixed End
Continuous Beam with Concentrated Moment at B
A continuous beam ABC is a structural element that is supported by multiple columns or supports. The beam is loaded with a concentrated moment at B, which causes bending stress in the beam. The end reaction at C is calculated as R, which is the force that is required to balance the load and keep the beam in equilibrium.
Fixed End Condition
If the end of the beam at C is fixed, the reaction at C will be different from the previous case. A fixed end condition means that the end of the beam is restrained from any movement, rotation or translation. This type of end condition creates a higher level of support compared to the simply supported end condition.
Reaction Calculation for Fixed End Condition
To calculate the reaction at end C for a fixed end condition, we need to consider the moment caused by the concentrated load at B. The moment is calculated by multiplying the load by the distance between the load and the fixed end. This moment creates an internal stress in the beam that resists the deformation caused by the load.
The reaction at end C is calculated by summing the moments and forces acting on the beam. The sum of the moments is zero because the beam is in equilibrium. Therefore, the sum of the forces is equal to zero. The reaction at end C is equal to the load at B plus the moment caused by the load, divided by the distance between B and C.
Conclusion
In summary, the reaction at end C of a continuous beam with a fixed end condition is calculated by summing the moments and forces acting on the beam. The fixed end condition creates a higher level of support compared to the simply supported end condition. The moment caused by the concentrated load at B creates an internal stress in the beam that resists the deformation caused by the load.