Solving indeterminate frame by moment distribution method

Problem 8-2

Use Moment distribution method to find the resultant end moments for the non-sway frame shown in figure 8-2(a). Also draw bending moment diagram. Take EI as constant for all the members of the frame.

Figure 8-2(a)


Step 1: The given rigid frame is non-sway because of lateral support at D. Consider each span (AB, BC, CD and CE) with both ends fixed and calculate the fixed-end moments as follows;

MAB = 0

MBA = 0

MBC = wL2 /12 = -6.67 kNm

MCB = -wL2 /12 = +6.67 kNm

MCD = PL/8 = -10 kNm

MDC = -PL/8 = +10 kNm

MCE = 0

MEC = 0

Step 2: Stiffness Coefficients

kAB = 4EI/L = 4EI/5 = 0.8EI

kBA = 4EI/L = 4EI/5 = 0.8EI

kBC = 4EI/L = 4EI/4 = EI

kCB = 4EI/L = 4EI/4 = EI

kCD = 4EI/L = 4EI/4 = EI

kDC = 4EI/L = 4EI/4 = EI

kCE = 4EI/L = 4EI/5 = 0.8EI

kEC = 4EI/L = 4EI/5 = 0.8EI

Step 3: Distribution factors

DAB = 0 (fixed support at the end)

DBA = 0.8EI/(0.8EI+EI) = 0.44

DBC = EI/(0.8EI+EI) = 0.56

DCB = EI/(EI+EI+0.8EI) =0.36

DCD = EI/(EI+EI+0.8EI) = 0.36

DCE = 0.8EI/(EI+EI+0.8EI) = 0.28

DDC = 0 (fixed support at the end)

DEC = 0 (fixed support at the end)

Calculation for moment distribution is shown in a systematic way in a tabular form. Each joint is balanced by distributing the unbalanced moment into the connected members  in proportion of distribution factors. These calculation steps for balancing of joints are shown with grey colour to show the illustration. The carry-over moments (half of the balancing moment at near end) are applied on the far end, e.g. carry-over half of the balancing moment from BA to AB, BC to CB, CB to BC, CD to DC and CE to EC etc.

(In case of mobile device please scroll horizontally to view the full width of table)

Table for Moment Distribution













Distribution Factors 0 0.44 0.56 0.36 0.28 0.36 0 0
Initial Fixed-end Moments 0 0 -6.67 +6.67 0 -10 +10 0
Balancing   6.67x0.44










Carry-over 1.47   0.6 1.87     0.6 0.47
Balancing   -0.6x0.44










Carry-over -0.132   -0.33 -0.168     -0.33 -0.26
Balancing   0.33x0.44










Carry-over 0.072   0.03 0.092     0.03 0.024
Balancing   -0.03x0.44










Carry-over -0.006   -0.016 -0.008     -0.016 -0.013
Final End-Moments 1.41 2.83 -2.83 8.98 0.51 -9.49 10.26 0.26

Resultant bending moment diagram in figure 8-2(b) is plotted by superposing the span moment diagram and support moment diagram.

Note: Please use our bending  moment calculator to get the values of span moments

      bending moment diagram for frame

                               (all values in kNm)

     (span moment in blue colour, support moment in red colour

                                 Figure 8-2(b)     

You can visit the following links of solved examples for Indeterminate Structures

Excellent Calculators

Stress Transformation Calculator
Calculate Principal Stress, Maximum shear stress and the their planes

Calculator for Moving Load Analysis
To determine Absolute Max. B.M. due to moving loads.

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
Contining Tall building worldwide

Forthcoming conferences
Contining 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