**Calculation of support reactions for overhanging beam**

**Problem 4-2**

The simply supported beam shown in figure 4-2(a) has overhanging portion on one side. Find the reactions at the supports.

**Figure 4-2(a)**

**Solution:**

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 ΣF_{x} = 0, ΣF_{y} = 0, ΣM_{z}
= 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:

ΣF_{x} = 0; **A**_{x}
= 0; (eq.
1)

ΣF_{y} = 0; **A**_{y} + **B**_{y}
– 25 – 5 × 4 = 0;

**A**_{y} + **B**_{y} = 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)*;

ΣM_{z} = 0; **B**_{y}
× 6 – 25 × 10 – 5 × 4 × 4 = 0 (eq. 3)

Solving eq. 3 yields **B**_{y}
= 55 kN;

Substituting the value of **B**_{y}
in eq. 2 gives **A**_{y} = –10 kN.

The –ve sign of reaction indicates that
**A _{y} **will be in the

You can also use our overhanging beam calculator to determine the values of support reactions

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