Calculation of the Statically Indeterminate Structure With Elastic Translational Support Based on the Moment Distribution Method

2021 ◽  
Vol 3 (3) ◽  
pp. 468-473
Author(s):  
Sun Yun
Keyword(s):  
Distribution Method ◽  
Moment Distribution ◽  
Moment Distribution Method ◽  
The Moment

scholarly journals A Matrix Formulation for the Moment Distribution Method Applied to Continuous Beams

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Arlindo Pires Lopes ◽  
Adriana Alencar Santos ◽  
Rogério Coelho Lopes
Keyword(s):  
Structural Analysis ◽  
Algebraic Equations ◽  
Displacement Method ◽  
Matrix Formulation ◽  
Distribution Method ◽  
Continuous Beams ◽  
Moment Distribution ◽  
Moment Distribution Method ◽  
Carry Over ◽  
The Moment

The Moment Distribution Method is a quite powerful hand method of structural analysis, in which the solution is obtained iteratively without even formulating the equations for the unknowns. It was formulated by Professor Cross in an era where computer facilities were not available to solve frame problems that normally require the solution of simultaneous algebraic equations. Its relevance today, in the era of personal computers, is in its insight on how a structure reacts to applied loads by rotating its nodes and thus distributing the loads in the form of member-end moments. Such an insight is the foundation of the modern displacement method. This work has a main objective to present an exact solution for the Moment Distribution Method through a matrix formulation using only one equation. The initial moments at the ends of the members and the distribution and carry-over factors are calculated from the elementary procedures of structural analysis. Four continuous beams are investigated to illustrate the applicability and accuracy of the proposed formulation. The use of a matrix formulation yields excellent results when compared with those in the literature or with a commercial structural program.

On the Solution of the Numerical Simultaneous Equations Arising in the Analysis of Redundant Structures

1945 ◽  
Vol 49 (411) ◽  
pp. 104-111
Author(s):  
F. J. Turton
Keyword(s):  
Strain Energy ◽  
Linear Equations ◽  
Simultaneous Equations ◽  
Distribution Method ◽  
Energy Applications ◽  
Moment Distribution ◽  
Simultaneous Linear Equations ◽  
Moment Distribution Method ◽  
Mathematical Accuracy ◽  
The Moment

The application of strain energy or slope-deflection methods in the analysis of redundant structures leads to a number of simultaneous linear equations with numerical coefficients; the equations may be obtained in such order that each successive equation contains one new unknown, until all the unknowns are so included. This is the only condition essential for the method to be described in the present paper, but the labour is much reduced in slope-deflection and strain energy applications by the fact that most (or all) of the equations contain very few of the unknowns. The method to be given reduces the solving of these equations to a column of successive evaluations, followed by the solution, by algebraic methods, of a small number of simultaneous equations; and a final column of evaluations. In the remaining paragraphs a number of problems are examined to show how the equations may be obtained in suitable sequence for the method to apply. Following an application to the determination of secondary stresses, the operations involved in the moment-distribution method and in this method are compared. A numerical example is worked out in the simple case of §2, and it is shown how any order of mathematical accuracy in the roots may be ensured, provided that sufficient figures have been retained to permit that accuracy.

Improved Moment Distribution Method and its Application

2013 ◽  
Vol 353-356 ◽  
pp. 3163-3166
Author(s):  
Shu Zhi Liu
Keyword(s):  
Exact Solution ◽  
Bending Stiffness ◽  
General Idea ◽  
Continuous Beam ◽  
Distribution Method ◽  
Moment Distribution ◽  
Moment Distribution Method ◽  
Internal Forces ◽  
The Moment

Change the general idea of the moment distribution method to analyze problems,not repeat fixed and relax joints to achieve a balance moment, but by the correction of the bending stiffness,deduced the moment carryover factor,moment once distributed and transferred twice you can get the moment exact solution.. Particularly suitable for the calculation of continuous beam internal forces and determination of envelope diagram and the influence lines of beam.

CORRESPONDENCE. THE MOMENT DISTRIBUTION METHOD.

1944 ◽  
Vol 22 (8) ◽  
pp. 431-433
Author(s):  
C E REYNOLDS ◽  
J A TODD ◽  
A E SEDDON
Keyword(s):  
Distribution Method ◽  
Moment Distribution ◽  
Moment Distribution Method ◽  
The Moment

scholarly journals ANALISIS DAN PERENCANAAN GEDUNG “STUDI KASUS PERENCANAAN GEDUNG BELAJAR PONDOK PESANTREN TAHFIDZ AL–QU’RAN (PPTQ) BERTINGKAT TIGA DESA SUNGAI RAYA KECAMATAN BATANG TUAKA KABUPATEN INDRAGIRI HILIR

2021 ◽  
Vol 1 (1) ◽  
pp. 10
Author(s):  
M. Yoga Ali Akbar
Keyword(s):  
Boarding School ◽  
Male Students ◽  
Lateral Loads ◽  
Distribution Method ◽  
Analysis Process ◽  
Moment Distribution ◽  
Moment Distribution Method ◽  
The Cross ◽  
The Moment ◽  
Fixed End

Abstract Building planning in this study is a three-story Islamic boarding school building planning. The building function in this planning is used for the male students' learning building, with planning data based on Permendiknas No. 24/2007. Structural analysis to calculate internal forces on the structure uses two methods, namely the Cross method and the Cantilever Method. The Cross method or also known as the moment distribution method is used to calculate the vertical forces acting on the structure, in the analysis process this method carries out a moment distribution and induction (cary over) of the primary moment (Fixed End Moment) for a number of rounds (iterations) in order to get balance at each knot point. While the cantilever method is used to calculate the horizontal force acting on the structure. The cantilever method is an approximate method for calculating the shear and moment forces developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads usually include wind loads and earthquake loads, which must be taken into account when planning a building structure. The assumptions used in this method are that the contraflexure points (or the moment diagram inflection points) in the vertical and horizontal sections are located at the midpoint. Abstrak Perencanaan gedung dalam penelitian ini adalah perencanaan gedung Pondok Pesantren bertingkat tiga. Fungsi gedung di perencanaan ini digunakan untuk gedung belajar santri putra, dengan data – data perencanaan berdasarkan Permendiknas No 24 Tahun 2007. Analisa struktur untuk menghitung gaya – gaya dalam pada struktur mengunakan dua metode yaitu metode Cross dan Metode Kantilever. Metode Cross atau biasa juga disebut metode distribusi momen digunakan untuk menghitung gaya – gaya vertikal yang bekerja pada struktur, dalam proses analisis metode ini melalukan distribusi momen dan induksi (cary over) terhadap momen primer  (Fixed End Momen) sebanyak beberapa putaran (iterasi) guna mendapatkan keseimbangan di setiap titik simpul. Sedangkan metode Kantilever digunakan untuk menghitung gaya Horizontal yang bekerja pada struktur. Metode Kantilever adalah metode perkiraan untuk menghitung gaya geser dan momen yang dikembangkan dalam balok dan kolom bingkai atau struktur karena beban lateral. Beban lateral yang diterapkan biasanya mencakup beban angin dan beban gempa, yang harus dipertimbangkan saat merencanaan struktur bangunan. Asumsi-asumsi yang digunakan dalam metode ini adalah bahwa titik-titik contraflexure (atau titik-titik infleksi diagram momen) di bagian vertikal dan horizontal terletak di titik tengah.  

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