**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

Bending Moment Calculator

Calculate bending moment & shear force for simply supported beam

Moment of Inertia Calculator

Calculate moment of inertia of plane sections e.g. channel, angle, tee etc.

Reinforced Concrete Calculator

Calculate the strength of Reinforced concrete beam

Moment Distribution Calculator

Solving indeterminate beams

Deflection & Slope Calculator

Calculate deflection and slope of simply supported beam for many load cases

Fixed Beam Calculator

Calculation tool for beanding moment and shear force for Fixed Beam for many load cases

BM & SF Calculator for Cantilever

Calculate SF & BM for Cantilever

Deflection & Slope Calculator for Cantilever

For many load cases of Cantilever

Overhanging beam calculator

For SF & BM of many load cases of overhanging beam

Civil Engineering Quiz

Test your knowledge on different topics of Civil Engineering

Research Papers

Research Papers, Thesis and Dissertation

List of skyscrapers of the world

Containing Tall buildings worldwide

Forthcoming conferences

Containing List of civil engineering conferences, seminar and workshops

Profile of Civil Engineers

Get to know about distinguished Civil Engineers

Professional Societies

Worldwide Civil Engineers Professional Societies

Keep visiting for getting updated or Join our mailing list

PleaseTell your Friends about us if you find our website useful