Moment Distribution Method

Displacement Method of Analysis (Moment Distribution Method)

The moment distribution method is the most suitable manual method for the analysis of continuous beams and plane frames. The method was presented by Prof. Hardy Cross of the USA in 1929.

The method consists in solving indirectly the equations of equilibrium as formulated in the slope deflection method without finding the displacements. This is an iterative procedure. This is also known as a relaxation method.

In this method the analysis begins by assuming each joint in the structure to be fixed. Then, by unlocking and locking each joint in succession, the internal moments at the joints are distributed and balanced until the joints have rotated to the final and nearly positions. The following examples has been given to illustrate the basic concept.

Sign Convention

The clockwise moment is taken as +ve and the anti-clockwise moment is taken as -ve i.e., the sign convention is the same as that in slope deflection method for member end moment calculation.

Member Stiffness Factor

Stiffness M/θ = K = 4EI/l and θ = Ml/4EI

Stiffness M/θ = K = 3EI/l and θ = Ml/3EI

Joint Stiffness Factor

As joint A is rigidly connected, all member at joint A will rotate by the same amount θA. If a moment M is applied at joint A the moment gets distributed in all the connected members. As all connected members rotate by same amount θA at A. We have-

M = (4EI3θA/l3 + 4EI2θA/l2 + 4EI1θA/l1)

M/ θA = K1 + K2 + K3 = Joint Stiffness Factor (K)

Distribution Factor (D.F.)

If a moment M is applied at joint A due to which the joint rotates by θA then,

Moment Distributed in AC= 4EI2θA/l2 = KAC θA = MDAC

Moment Distributed in AB= 3EI1θA/l1 = KAB θA = MDAB

MDAD : MDAC : MDAB = I3/l3 : I2/l2 : 3I1/4l1

Where,

I3/l3 = Relative stiffness of AD

I2/l2 = Relative stiffness of AC

3I1/4l1 = Relative stiffness of AB

Relative Stiffness when far end is fixed = I/l

Relative Stiffness when far end is hinged = 3I/4l

Distribution Factor of a Member = Stiffness of member/Total Stiffness of all members at the joint

Carry Over Factor

When M moment is applied at pin, Moment carried over to fixed far end= M/2

Carry Over Factor= Carried over moment/Applied moment

However, In the following case, carry over factor = 0

Soil: Definition and Names of Various Types of Soil

The term ‘soil’ in soil engineering is defined as an unconsolidated material, composed of solid particles, produced by the disintegration of rocks. The void space between the particles may contain air, water or both. The soil particles may contain organic matter.

Continue Reading Soil: Definition and Names of Various Types of Soil

Bricks: Uses, Size, Weight, Frog, Types, and Much More

What are Bricks? Bricks are one of the oldest building materials and it’s extensively used at present as a loading material in construction methods because of its durability, strength, reliability, low cost, easy availability, etc. Bricks are manufactured by molding burnt clay or a mixture of sand and lime or of Portland cement concrete, in…

Continue Reading Bricks: Uses, Size, Weight, Frog, Types, and Much More

Water Proofing Materials, Damp-Proofing Course, and much more

Water Proofing Materials Dampness in a building is the main cause of the deterioration of the building as well as for the ill-health of the occupants. The damp brickwork in the buildings is prone to fresh attack. Also, the soluble salts in bricks are liable to attack the cement mortar when the brickwork remains wet…

Continue Reading Water Proofing Materials, Damp-Proofing Course, and much more

Sound Insulation And Sound Insulating Materials

Sound Insulation A well-designed building should incorporate sound insulation to restrain the noise level. High noise conditions result in uncomfortable living conditions, mental strains, fatigue, and may even lead to a nervous breakdown or temporary deafness. Adequate insulation can be achieved by using sound-absorbing or sound repellent materials. Sound Insulating Materials Sound Insulating Materials fall…

Continue Reading Sound Insulation And Sound Insulating Materials

Heat Insulating Materials: Convection, Radiation, and Conduction

Heat Insulating Materials The purpose of thermal insulation is to restrict the heat transfer from warmer to cooler areas. Transfer of heat takes place by three processes- the convection, the radiation and, the conduction. Convection In convection, heat is transferred from one place to another by the movement and mixing of liquids or gases. Radiation…