Indeterminate Structure

1. Moment
Distribution
Method
Prepared By
Iftekhar Alam Dipto
BSc in Civil & Environmental Engineering (IUT)
PAGE 1

2. Concept of Analyzing Indeterminate Structures
PAGE 2
The structure shown in the right side is
typical for a concrete building frame. The
structure has rigid connections between all
of the members, and this results in 27
degrees of static indeterminacy and 15
degrees of freedom.
This system would clearly be all but
impossible to analyze using the Force
method or the Slope-deflection method.
Prior to the development of the Moment
distribution method in 1932, there was
simply no practical way to analyze such a
system.

3. Introduction
 Force method was good for structure with a small number
of degrees of indeterminacy, regardless of how many
degrees-of-freedom the system has.
 The Slope-deflection method was good for structures with a
small number of degrees-of-freedom, regardless of how
many degrees of indeterminacy the system has.
 The Moment distribution method is an iterative method
that gets around the problem of too many degrees of
indeterminacy or too many degrees of freedom. Using
moment distribution, we can analyze highly indeterminate
structures with many degrees of freedom by hand.
 The moment distribution method is also called the Hardy
Cross method after its inventor, an engineering professor
named Hardy Cross.
PAGE 3

4. Moment
Distribution
Method
Concepts
PAGE 4
The method of moment distribution is this:
(a) Imagine all joints in the structure held so that they cannot
rotate and compute the moments at the ends of the member
for this condition;
(b) At each joint distribute the unbalanced fixed-end moment
among the connecting members in proportion to the constant
for each member defined as "stiffness";
(c) Multiply the moment distributed to each member at a joint
by the carry-over factor at that end of the member and set
this product at the other end of the member;
(d) Distribute these moments just "carried over";
(e) Repeat the process until the moments to be carried over
are small enough to be neglected; and
(f) Add all moments -- fixed-end moments, distributed
moments, moments carried over -- at each end of each
member to obtain the true moment at the end
In his own words, Hardy Cross summarizes the
moment-distribution method as follows:

5. 5 Main Steps
Stiffness Factors - K
Distribution Factors - DF
Fixed End Moments - FEM
Moment Distribution - MD
Carry Over - CO
PAGE 5

6. Stiffness Factors - K
The stiffness will depend on the type of
boundary condition at the opposite end of the
member, whether it is fixed or pinned.
PAGE 6
Bending Stiffness:
The bending stiffness (EI/L) of a member is
represented as the flexural rigidity of the
member (product of the modulus of elasticity (E)
and the second moment of area (I)) divided by
the length (L) of the member.

7. Distribution Factors - DF
 When a joint is being released and begins to rotate
under the unbalanced moment, resisting forces
develop at each member framed together at the joint.
Although the total resistance is equal to the
unbalanced moment, the magnitudes of resisting
forces developed at each member differ by the
members' bending stiffness. Distribution factors can be
defined as the proportions of the unbalanced
moments carried by each of the members.
PAGE 7
 Determine the distribution factors for each
member at each node based on relative stiffness
of the members using equation
 Use a distribution factor of zero for a fixed
support and 1.0 for a pinned support with only
one connected member.

8. Fixed End
Moments - FEM
PAGE 8

9. Moment Distribution & Carry Over
 For each member that the moment has been distributed to, carry over some of the moment to
the opposite end of the member according to equations
 For a member with a fixed end opposite (a regular locked node), carry over half of the moment
that was applied by the distribution. For a member with a pinned end opposite (where there are
no other members connected to that pin) do not carry over any moment.
PAGE 9

10. PAGE 10

11. PAGE 11

12. PAGE 12