scholarly journals Comparative Analysis and Design of Bridge Pier for Various Geometries Along Height Comparing the Parameters Deflection and Bending Stresses

2021 ◽  
Vol 9 (12) ◽  
pp. 571-580
Author(s):  
Prof. G. C. Jawalkar
Keyword(s):  
Bending Moment ◽  
Moment Equation ◽  
Second Order ◽  
Bridge Pier ◽  
Column Buckling ◽  
Circular Section ◽  
Analysis And Design ◽  
Order Analysis ◽  
Bending Stresses ◽  
Slender Column

Abstract: Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

scholarly journals Comparative Analysis and Design of Bridge Pier for various Geometries along height

2021 ◽  
Vol 9 (12) ◽  
pp. 431-440
Author(s):  
Prof. G.C. Jawalkar
Keyword(s):  
Bending Moment ◽  
Moment Equation ◽  
Second Order ◽  
Bridge Pier ◽  
Biaxial Bending ◽  
Column Buckling ◽  
Circular Section ◽  
Analysis And Design ◽  
Order Analysis ◽  
Slender Column

Abstract: Slender member is subjected to axial load and biaxial bending moment and fails due to buckling. This buckling is caused due to slenderness effect also known as ‘P∆’ effect. This buckling gives rise to excessive bending moment occurring at a point of maximum deflection. This additional bending moment is considered in second order analysis. The objective of the research reported in this paper is to formulate bending moment equation by using beam column theory and to study the behaviour of solid circular section and hollow circular section of bridge pier. The optimization in area of cross section is done by providing a combination of solid and hollow circular section in place of a solid circular section of pier within permissible limits. A comparative study on behaviour for all three conditions is been carried out. Keywords: slender column, buckling, ‘P∆’ effect, beam-column, second order analysis, bridge pier.

STABILITY AND SIMULATION-BASED DESIGN OF STEEL SCAFFOLDING WITHOUT USING THE EFFECTIVE LENGTH METHOD

2003 ◽  
Vol 03 (04) ◽  
pp. 443-460 ◽  
Author(s):  
S. L. CHAN ◽  
A. Y. T. CHU ◽  
F. G. ALBERMANI
Keyword(s):  
Bending Moment ◽  
Nonlinear Problems ◽  
Second Order ◽  
Effective Length ◽  
Analysis And Design ◽  
Order Analysis ◽  
Effective Length Factor ◽  
Highly Nonlinear ◽  
Reliable Design ◽  
Effective Length Method

A robust computer procedure for the reliable design of scaffolding systems is proposed. The design of scaffolding is not detailed in design codes and considered by many researchers and engineers as intractable. The proposed method is based on the classical stability function, which performs excellently in highly nonlinear problems. The method is employed to predict the ultimate design load capacities of four tested 3-storey steel scaffolding units, and for the design of a 30 m×20 m×1.3 m 3-dimensional scaffolding system. As the approach is based on the rigorous second-order analysis allowing for the P-δ and P-Δ effects and for notional disturbance forces, no assumption of effective length is required. It is superior to the conventional second-order analysis of plotting only the bending moment diagram with allowance for P-Δ effect since it considers both P-Δ and P-δ effects such that section capacity check is adequate for strength and stability checking. The proposed method can be applied to large deflection and stability analysis and design of practical scaffolding systems in place of the conventional and unreliable effective length method which carries the disadvantages of uncertain assumption of effective length factor (L e /L).

scholarly journals Alternative Design Procedure for RC-Braced Long Columns Based on New Moment Magnifiers Matrix

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Mohamed Farouk ◽  
Majed Alzara ◽  
A. Ehab ◽  
A. M. Yosri
Keyword(s):  
Flexural Rigidity ◽  
Design Procedure ◽  
Bending Moment ◽  
Order Effect ◽  
Second Order ◽  
Effective Length ◽  
Column Height ◽  
Order Effects ◽  
Order Analysis ◽  
Proposed Model

Based on modified methods for the results of first-order analysis of RC columns, different codes approximate the second-order effects by using equations focusing on the maximum additional moment through the column height. These equations did not refer to the additional moments between the column and the connected beam, only the effect of the connected beams is taken into consideration by dealing with the effective length of the column, not the total length. Moreover, these equations did not take into account the second-order effect, which is caused by axial force and the inverse moments due to beam restriction for the column ends. This paper presents a new moment magnifiers matrix for the additional moments at the connection between braced columns and the connected beams as a simplified computation that can be used in the design procedure. That is through an equation based on transforming the original long column in second-order analysis to an equivalent isolated column. The equivalent column was represented as an element restricted with rotational spring support at its ends, and it is subjected to lateral distributed loads that have the same influence of the second-order effect on the induced additional moments in the long column. The suggested equivalent column can be used to form the additional bending moment diagram, also to compute the additional deformations as well. Numerous factors were analyzed linearly by using the presented new moment magnifiers matrix and finite element method, and the results proved the efficiency of the proposed model. Although the presented suggested model is based on the isolated analysis of the long column, the effect of the additional moments in the adjacent long column can be considered by presented two suggestions to improve the model. Also, development was proceeded on the model by modifying the flexural rigidity (EI) which is recommended in ACI to appropriate the time of failure. The additional moment values of the developed model were close to the values calculated by the ACI equation.

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