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.

overhanging beam

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 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.

free-body diagram

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

You can visit the following links of solved examples on Bending moment and shear force calculations and plotting of diagrams




Excellent Calculators

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

More Links

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

Search our website for more...

PleaseTell your Friends about us if you find our website useful

Other Useful Links

Join Our Mailing List