Calculation of support reactions for overhanging beam
The simply supported beam shown in figure 4-2(a) has overhanging portion on one side. Find the reactions at the supports.
The given beam has a hinged support at A and a roller support at B. The free-body diagram is given in figure 4-2(b), which shows 2 reactions at A and one reaction at B. (The x-axis and y-axis are as shown in the figure and the z-axis is perpendicular to the x-y plane.) There are three equations of static equilibrium ΣFx = 0, ΣFy = 0, ΣMz = 0; available for this 2-dimensional structure. The number of unknown reaction components is equal to equations of static equilibrium. Therefore this beam is statically determinate.
Figure 4-2(b) free body diagram
Applying equations of static equilibrium:
ΣFx = 0; Ax = 0; (eq. 1)
ΣFy = 0; Ay + By 25 5 × 4 = 0;
Ay + By = 45 kN; (eq. 2)
Considering z-axis passing through A, and taking moment of all the forces about z-axis (taking clockwise ve and anticlockwise +ve);
ΣMz = 0; By × 6 25 × 10 5 × 4 × 4 = 0 (eq. 3)
Solving eq. 3 yields By = 55 kN;
Substituting the value of By in eq. 2 gives Ay = 10 kN.
The ve sign of reaction indicates that Ay will be in the downward direction instead of upward as shown in the free-body diagram.
You can also use our overhanging beam calculator to determine the values of support reactions
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