A BEAM THEORY WITH CROSS-SECTIONAL DEFORMATION DUE TO BOTH SHEAR LAG AND TRANSVERSE SHEAR

2021 ◽  
Vol 77 (1) ◽  
pp. 1-11
Author(s):  
Isao SAIKI ◽  
Xun ZHENG
Keyword(s):  
Transverse Shear ◽  
Beam Theory ◽  
Shear Lag ◽  
Cross Sectional

scholarly journals On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures

2019 ◽  
Vol 69 (2) ◽  
pp. 27-56
Author(s):  
Kugler Stephan ◽  
Fotiu Peter ◽  
Murín Justín
Keyword(s):  
Transverse Shear ◽  
Reference Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Bench Mark ◽  
Cross Sectional ◽  
Beam Structures ◽  
Novel Approach ◽  
The Cross ◽  
Constitutive Parameters

AbstractThe application of first order shear beam theory in the analysis of beam structures made of functionally graded materials requires the access to homogenized stiffness quantities. These quantities depend on the cross-sectional shape and on the spatial variation of constitutive parameters. Some of these stiffness quantities can be evaluated easily by simple integration, however, the access to transverse shear stiffnesses and to stiffness quantities regarding warping torsion is typically cumbersome. In this contribution a novel approach for their evaluation is proposed, which is based on a reference beam problem. Here, we restrict ourselves to double symmetric cross-sections, however, a generalization of the proposed method to the arbitrary case is obvious. Besides that, a novel approach to cover non-uniform warping torsion is included. The proposed method is efficient, since the discretization of the cross-section suffices, and accurate as can be shown in challenging bench mark problems.

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

2016 ◽  
Vol 22 (10) ◽  
pp. 2011-2039 ◽  
Author(s):  
Gerard Taig ◽  
Gianluca Ranzi
Keyword(s):  
Structural Response ◽  
Beam Theory ◽  
Element Model ◽  
Composite Beams ◽  
Cross Sectional ◽  
Shear Connections ◽  
Dynamic Analyses ◽  
Partial Interaction ◽  
Deformation Modes ◽  
Generalised Beam Theory

This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

GBT Analysis of Steel-Concrete Composite Beams: Recent Developments

2020 ◽  
Vol 20 (13) ◽  
pp. 2041007
Author(s):  
Rodrigo Gonçalves ◽  
Dinar Camotim ◽  
David Henriques
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Composite Beams ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Shear Lag ◽  
Buckling Mode ◽  
Concrete Cracking ◽  
Lag Effects ◽  
Recent Developments

This paper reports the most recent developments concerning Generalized Beam Theory (GBT) formulations, and corresponding finite element implementations, for steel-concrete composite beams. These formulations are able to perform the following types of analysis: (i) materially nonlinear analysis, to calculate the beam load-displacement response, up to collapse, including steel plasticity, concrete cracking/crushing and shear lag effects, (ii) bifurcation (linear stability) analysis, to obtain local/distortional bifurcation loads and buckling mode shapes of beams subjected to negative (hogging) bending, accounting for shear lag and concrete cracking effects and (iii) long-term service analysis including creep, cracking and arbitrary cross-section deformation (which includes shear lag) effects. The potential (computational efficiency and accuracy) of the proposed GBT-based finite elements is illustrated through several numerical examples. For comparison purposes, results obtained with standard finite strip and shell/brick finite element models are provided.

scholarly journals Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

2020 ◽  
Vol 10 (15) ◽  
pp. 5245
Author(s):  
Chunfeng Wan ◽  
Huachen Jiang ◽  
Liyu Xie ◽  
Caiqian Yang ◽  
Youliang Ding ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Cross Sections ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Timoshenko Beam Theory ◽  
Rotary Inertia ◽  
Cross Sectional

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.

Modelling of Rotating Twisted Blades as 1D Continuum

2016 ◽  
Vol 821 ◽  
pp. 183-190
Author(s):  
Jan Brůha ◽  
Drahomír Rychecký
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Beam Theory ◽  
Parameter Tuning ◽  
Finite Element Models ◽  
Cross Sectional ◽  
One Dimensional ◽  
Rayleigh Beam ◽  
Twisted Blade ◽  
Sectional Parameters

Presented paper deals with modelling of a twisted blade with rhombic shroud as one-dimensional continuum by means of Rayleigh beam finite elements with varying cross-sectional parameters along the finite elements. The blade is clamped into a rotating rigid disk and the shroud is considered to be a rigid body. Since the finite element models based on the Rayleigh beam theory tend to slightly overestimate natural frequencies and underestimate deflections in comparison with finite element models including shear deformation effects, parameter tuning of the blade is performed.

scholarly journals An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2198 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Do Van Thom
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Beam Theory ◽  
Beam Element ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Beam ◽  
Transverse Shear Stresses ◽  
Power Law Index ◽  
Transverse Shear Strains

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

On the Significance of the Inclusion of the Effect of Transverse Normal Strain in Problems Involving Beams With Surface Constraints

1975 ◽  
Vol 42 (1) ◽  
pp. 127-132 ◽  
Author(s):  
F. Essenburg
Keyword(s):  
Shear Deformation ◽  
General Problem ◽  
Transverse Shear ◽  
Beam Theory ◽  
Transverse Shear Deformation ◽  
Normal Strain ◽  
Rectangular Section ◽  
Surface Constraints ◽  
Transverse Normal Strain

The general problem of a beam of rectangular section with displacement components prescribed over portions of its top and bottom surfaces is considered. A beam theory which includes the effect of transverse normal strain (as well as the effect of transverse shear deformation) is developed and the advantages of applying this theory to the class of problems considered is examined by means of an example.

Long-term dispersion of contaminants in small estuaries

1977 ◽  
Vol 82 (1) ◽  
pp. 129-146 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Transverse Shear ◽  
Discharge Rate ◽  
Water Discharge ◽  
Vertical Shear ◽  
Tidal Elevation ◽  
Cross Sectional ◽  
Dominant Mechanism ◽  
Contaminant Dispersion ◽  
Fresh Water Discharge

It is shown that the use of axes moving with the tide (Shinoharaet al.1969) simplifies the analysis of contaminant dispersion in estuaries. Attention is restricted to estuaries which are small in the sense that cross-sectional mixing is rapid and that the tidal elevation can be taken to be constant along the estuary. In agreement with the work of Fischer (1972a, b) it is found that the dominant mechanism for dispersion is the transverse shear and not the vertical shear. Results are presented to illustrate the dependence of the upstream penetration of salt upon the estuary geometry as well as upon the fresh-water discharge rate.

scholarly journals Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal ◽  
N. S. Naik
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Laminated Composite ◽  
Beam Theory ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Transverse Displacement ◽  
Sandwich Beams ◽  
Bending Analysis

AbstractA trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations and boundary conditions are obtained by using the principle of virtual work. To demonstrate the validity of present theory it is applied to the bending analysis of laminated composite and sandwich beams. The numerical results of displacements and stresses obtained by using present theory are presented and compared with those of other trigonometric theories available in literature along with elasticity solution wherever possible.

Analytical Simulation of the Composite Ice Wall

1989 ◽  
Vol 111 (3) ◽  
pp. 174-180 ◽  
Author(s):  
P. Corder ◽  
T. Kozik
Keyword(s):  
Shear Stress ◽  
Closed Form ◽  
Normal Stress ◽  
Transverse Shear ◽  
Parametric Study ◽  
Beam Theory ◽  
Transverse Shear Stress ◽  
Transverse Normal Stress ◽  
Analytical Simulation ◽  
Sandwich Configuration

A system of linear, closed-form stress equations for a steel-concrete-steel sandwich configuration, i.e., the “Composite Ice Wall,” was derived incorporating a formulation of classical beam theory. The stress terms include the longitudinal normal stress, the transverse shear stress and the transverse normal stress. These equations were programmed using Pascal and a parametric study was conducted. Some of the results are included herein. The analytical model produces principal stress contours and centerline deflections very similar to those in the classical beam for comparable pressure loadings.

Sign in / Sign up

Export Citation Format

Share Document