Stiffness, carry over factor, distribution and carryover of moments

1. SNS COLLEGE OF ENGINEERING
Kurumbapalayam (Po), Coimbatore – 641 107
An Autonomous Institution
Accredited by NBA – AICTE and Accredited by NAAC – UGC with ‘A’ Grade
Approved by AICTE, New Delhi & Affiliated to Anna University, Chennai
DEPARTMENT OF CIVIL ENGINEERING
COURSE NAME: CE8502 – STRUCTURAL ANALYSIS I
III YEAR/V SEMESTER
Unit 3 – Moment Distribution Method
Topic 1 : Stiffness, carry over factor, distribution and carryover of moments

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
 Introduced by Professor Hardy cross in 1932.
It’s tackling indeterminate beams and rigid frames.
It’s an Iterative (மறுபயன்பாடு) technique.
Introduction

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Four specialized terms

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Fixed end Moments
Assume fixed ends at given all frame/Beam
Fixed end moments based on load acting on
the member.
It’s exerted by the support on the beam
ends.

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Standard Fixed end Moments

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Standard Fixed end Moments

7. The force required to produce a unit displacement in a
member or structure.
The moment required to produce unit rotation at a
specified point in a beam or structure.
The torque needed to produce unit twist.
In this method we need to know the moment required to
produce a unit clockwise rotation at a support point in a
beam.
Stiffness is denoted as k
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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Relative stiffness

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Relative stiffness
K = 4 EI/l (Far end is fixed ; Fig. (a) )
K = 3 EI/l (Far end is hinged; Fig. (b) )
Note: k will be large if E or / and I are large. When k is less when l is more.

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Carry over
To analysis the effects of applying imaginary moments at a specified
point.
In below figure, when it receive a moment M at A, will develop at B a
moment of M/2 (Half).
If the far end B were hinged, the C.O.F will be zero.

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Distribution Factor
A moment which tends to rotate without translation a joint to which several
members are connected will be divided amongst the connected members in a
proportion to their stiffness's.
Joint A by an external moment M in below

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Distribution Factor
.
i. The rotation of each member at A is obviously θ.
ii. The moments MAB , MAC , MAD (Summing up to M) will be in the ration
k1:k2:k3
Hence,
The factors ki / ∑k are called distribution factors.
MAB = (k1/∑k) . M
MAC = (k2/∑k) . M
MAD = (k3/∑k) . M

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SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil
Thank You
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