Calculation of support reactions in frame

under the action of the load system:

• • force F=10kN;

  • moment m=40kNm;

  • uniformly distributed load q=20kN/m,

size a=3m.

Reaction calculation

Before starting the solution of the task, we transfer the numerical data of the loads to the design scheme and designate the characteristic points (sections) of the frame with the letters A, B, C, D and E.

The support reactions of the frame will be determined from the equilibrium condition of a plane system of forces.

Our short video tutorial on calculating the reactions of beam supports:

In the pivotally motionless support (point A) two reaction components can arise – horizontal H_A and vertical R_A, and in the pivotally movable support (point A) only one reaction – vertical R_B.

About reactions in articulated supports

At this stage of the solution, these reactions can be directed arbitrarily, for example:

To find the three unknown forces, we need three static equations: two equations of the sum of the moments relative to the control points and the sum of the projections of all the forces on the horizontal axis X, which should be zero.

We write them down:

From each equation we express and find the corresponding value of the support reaction:

The “-” sign of the R_B reaction indicates that the arbitrarily chosen direction turned out to be wrong, and it must be redirected in the opposite direction, while changing the sign to positive.

In tasks of this kind, after calculating the reactions in the supports, it is strongly recommended to check the obtained values, since even a small error in further calculations can lead to an incorrect result.

Reaction check

We perform an arithmetic test of the reactions by writing the sum of the moments relative to, for example, the middle of the CD crossbar (point K):

Identity is fulfilled, which means reactions are defined correctly.

After calculating and checking the support reactions, you can begin to build diagrams of internal force factors in the frames.