Home   Tell-A-Friend    Discussion Board   Contact Us

civil engineer

Treasure of Civil Engineering Resources

Course materials, Books, Computer software, Quiz,  Conferences, Journals, Research theses, Jobs, Products, Services etc.

                    Slope and deflection calculations- solved example for Simply supported beam

 

Problem 6-2

Use integration method to determine the values of slope and deflection at 5m from the left support due to imposed load as shown in figure 6-2(a). The material of beam has modulus of elasticity as 200 GPa. The beam cross-section is I-shaped with top and bottom flange width as 250 mm and thickness 20 mm, web height as 300 mm and web thickness as 15 mm.

simply supported beam

Figure 6-2(a)

Solution:

The loading is not same throughout the span, therefore we use Macaulay's Method for finding slope and deflection of the given beam.

The given beam has two unknown reaction components which are calculated in Prob 4-1 as  Ay = 66 kN and By = 24 kN;

The equivalent loading is shown in figure 6-2(b).The differential equation of elastic curve for this  beam can be written as follows;

 EI (d2y/dx2) = 66[x] - 20[x]2 /2 +20[x-4]2/2 - 10[x-8]         Eq. 1

Featured Links

Moment Distribution CalculatorNew

Solving Indeterminate Beams with different loads

Fixed Beam CalculatorNew

Fixed end moment, bending moment & reaction calculation for fixed beam

Moment of Inertia calculatorNew

For different sections including I-section and T-section.

Deflection Calculator

Easy to use calculator for different loads on beams

Problem SolverNew

A collection of illustrated solved examples for civil engineers.

RC Beam CalculatorNew

Calculate the strength of reinforced concrete beams

Bending Moment calculatorNew

Calculate Bending moments for simply supported beams

CE QUIZNew

A collection of quiz in different areas of civil engineering

Figure 6-2(b)

Integrating Eq. 1 we get;

EI(dy/dx) = 66[x]2/2 - 20[x]3 /6 +20[x-4]3/6 - 10[x-8]2/2 +C1     Eq.2

We do not have any information about slope at the ends,

We continue integrating Eq. 2 for finding deflection;

EIy = 66[x]3/6 - 20[x]4 /24 +20[x-4]4/24 - 10[x-8]3/6 +C1x + C2

Now apply the condition for deflection at the supports;

at x=0, y=0 (neglect the terms which become negative with x=0)

we get C2=0;

Further at x=10, y=0; we get

0=11000 - 200000/24 + 1080 - 80/6 + 10C1

C1= -374.66

Therefore the equation for slope can be written as

EI(dy/dx) = 66[x]2/2 - 20[x]3 /6 +20[x-4]3/6 - 10[x-8]2/2 - 374.66

and the equation for deflection would be

EIy = 66[x]3/6 - 20[x]4 /24 +20[x-4]4/24 - 10[x-8]3/6 - 374.66x

Slope at x=5;

   dy/dx = (37)/EI

Deflection at x=5;

   y = (- 1018)/EI

The value of moment of inertia can be calculated by using moment of inertia calculator

  Ixx = 29008.3 cm4

  EI= (200x109 N/m2)x(29008.3 cm4 ) = 58016.6 kN m2

substituting the value of EI in the expressions for slope and deflection we get;

  dy/dx = 37/58016.6 = 0.00064 rad.

   y = - 1018/58016.6 = - 0.0175 m (negative sign indicates that the deflection is downward)

You can also use our Slope deflection calculator for different combinations of load.

For other problems please visit our Problem SolverNew

CE HorizonNew

Online Civil Engineering Journal and Magazine

Profile of Civil EngineersNew

Get to know about distinguished civil engineers

 
 

If you don't find the required information please suggest us We are updating the website regularly.

Join the mailing list to get informed about new products or links

 

Applied Mechanics 

Structural Analysis 

Design of Structures

Construction Materials

Engineering Graphics

Disaster Management

Skyscrapers

Geotechnics

Transportation

Land Surveying

Hydraulics

Environmental Engineering

Irrigation Engineering

Offshore Engineering

Construction Management 

Quantity Surveying

Construction Disputes

Construction Technology

Construction Equipments

Research Papers

Journals & Magazines

Construction Companies

Consultants

Professional Societies

Computer Software 

Conferences

Photo Album

Home

Tell-a-friend

Join us

Job Search

Book Store

Scholarships

Colleges & Universities

Learning Support

Last updated on Tuesday January 21, 2014