Home   Tell-A-Friend       Contact Us

civil engineer

Treasure of Civil Engineering Resources
Course materials, Books, Computer software, Quiz,  Conferences, Journals, Research theses, Jobs, Products, Services etc.
Direct Integration method for slope and deflection of beam  

Integration method

(a) Direct Integration; This method is based on the differential equation of elastic curve.

Integrating once the above equation of elastic curve gives an equation in terms of dv/dx with an unknown constant c1as follows;

EI (dv/dx) = Mx +c1

the value of constant c1 can be determined by applying the conditions of slope and/or deflection at some known points of the beam.

Similarly, integration of the equation again will give an equation in terms of "v" with an unknown constant c2 as given below;

EI v = Mx2/2 + c1x + c2

The value of constant c2 can be determined by applying the conditions of deflection at some known points.  

Featured Links

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

Reinforced concreteNew

Analysis and design of reinforced concrete structures

Bending Moment calculatorNew

Calculate Bending moments for simply supported beams


A collection of quiz in different areas of civil engineering

Profile of Civil EngineersNew

Get to know about distinguished civil engineers

CE HorizonNew

Online Civil Engineering Journal and Magazine

(b) Macaulay's method; This method is modified form of integration method and used when the loading is discontinuous and/or discrete. In other words we can say that a single equation is not sufficient to find bending moment along the span of the beam. In this method we put all the terms containing x into square bracket and we integrate the bracket not "x". During calculation for the values of slope and deflection, any bracket with negative value is to be ignored. An equivalent loading is required to be applied in case of uniformly distributed load. See example 6-1 and  6-2 for more explanations.

Use our Deflection Calculator Easy to use calculator for different loads on beams

Moment Distribution CalculatorNew

Solving Indeterminate Beams with different loads

RC Beam CalculatorNew

Calculate the strength of reinforced concrete beams

See more about bending moment and shearing force

Quiz on Structural Analysis

Quiz on Structural Design

Visit Problem Solver  for solved examples on deflection


Tell-A-Friend about civil engineering resources

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



Land Surveying


Environmental Engineering

Irrigation Engineering

Offshore Engineering

Construction Management 

Quantity Surveying

Construction Disputes

Construction Technology

Construction Equipments

Research Papers

Journals & Magazines

Construction Companies


Professional Societies

Computer Software 


Photo Album



Join us

Job Search

Book Store


Colleges & Universities

Learning Support

Last updated on Thursday January 31, 2013