Moment distribution method - Structural Analysis
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This document discusses the moment distribution method for analyzing indeterminate beams and rigid frames. It introduces four key terms used in this method: fixed end moments, which are exerted by supports; stiffness, which is a measure of a member's resistance to deformation; carry over factor, which describes how moments are distributed between members; and distribution factor, which indicates what proportion of an applied moment will be distributed to each member based on their relative stiffnesses. The document provides examples and explanations of each term.
Moment distribution method - Structural Analysis
- 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
- 2. 12/4/2020 2/12 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Introduced by Professor Hardy cross in 1932. Its tackling indeterminate beams and rigid frames. Its an Iterative (牀牀園牀牀牀牆牀牀鉦牆) technique. Introduction
- 3. 12/4/2020 3/12 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Four specialized terms
- 4. 12/4/2020 4/12SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Fixed end Moments Assume fixed ends at given all frame/Beam Fixed end moments based on load acting on the member. Its exerted by the support on the beam ends.
- 5. 12/4/2020 5/12 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Standard Fixed end Moments
- 6. 12/4/2020 6/12SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil 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 12/4/2020 7/12 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Relative stiffness
- 8. 12/4/2020 8/12 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.
- 9. 12/4/2020 9/12 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.
- 10. 12/4/2020 10/12 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
- 11. 12/4/2020 11/12 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Distribution Factor . i. The rotation of each member at A is obviously 慮. 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
- 12. 12/4/2020 12/12 SNSCE/ Civil Engg /V sem / Shanmugasundaram N/ Ap/Civil Thank You Education is the movement from darkness to light - Allan Bloom