Camptograms for Beams in Compression

1947 ◽  
Vol 14 (3) ◽  
pp. A202-A208
Author(s):  
V. Rojansky ◽  
R. A. Beth
Keyword(s):  
Graphical Method ◽  
Flexural Rigidity ◽  
Bending Moment ◽  
Transverse Load ◽  
Circular Arc ◽  
Usual Assumption ◽  
Transverse Loads ◽  
Distributed Load ◽  
Circular Arcs ◽  
Stepwise Variation

Abstract Under the usual assumption that the square of the slope of the beam may be neglected compared to unity, the authors show that if the bending moment M is used as ordinate and a quantity proportional to dM/dx as abscissa, then the curve representing an axially compressed uniform beam carrying a uniformly distributed transverse load is a circular arc or a sequence of circular arcs. This result leads to a graphical method for evaluating bending moment. The procedure is illustrated by examples which include external torques, concentrated transverse loads, built-in ends, stepwise variation of distributed load, stepwise variation of flexural rigidity, and a protruding end. The diagrams, named “camptograms,” are simpler to draw and to interpret than the polar diagrams currently used for the same purpose. The construction of camptograms representing the slope and the deflection of the beam is outlined.

The Torsionless Bending of a Hollow Beam by a Transverse Load

1937 ◽  
Vol 4 (1) ◽  
pp. A25-A30
Author(s):  
W. L. Schwalbe
Keyword(s):  
Cross Sections ◽  
Equilateral Triangle ◽  
Bending Moment ◽  
Longitudinal Section ◽  
Transverse Load ◽  
Shearing Stress ◽  
Numerical Work ◽  
Hollow Beam ◽  
Transverse Loads ◽  
Hollow Beams

Abstract The author discusses the bending of hollow beams when subjected to transverse loads, and points out that shearing stresses and strains in the cross sections are necessary, and a particular longitudinal section remains plane only if the resultant of the shearing stress, and hence the plane of the applied bending moment, possesses a particular location. The author determines the location of this resultant shearing stress by applying a method based on St. Venant’s theory. Applications of the method are made to two hollow sections. One of the sections is that of an equilateral triangle which serves as a measure of accuracy for the numerical work presented by the author, since the location of the resultant of the shearing stresses is known by symmetry.

The Bent Strut with Variable Cross Section

1941 ◽  
Vol 45 (362) ◽  
pp. 51-66 ◽  
Author(s):  
Jean Drymael
Keyword(s):  
Cross Section ◽  
Axial Load ◽  
Graphical Method ◽  
Variable Cross Section ◽  
Transverse Load ◽  
Variable Cross ◽  
Transverse Loads ◽  
Variable Section

SummaryA graphical method is developed for solving the problem of the beam with variable section, bent by transverse loads and an axial load. The latter may be either tensile or compressive. The beam on statically determinate supports is first dealt with, successively as regards the stress and the deformation. Then a similar procedure is followed for a beam with redundant supports. Finally, the case is studied when there is no transverse load at all, that is buckling only.

Finite Element Modeling of Self-Loosening of Bolted Joints

2004 ◽  
Author(s):  
Ming Zhang ◽  
Yanyao Jiang ◽  
Chu-Hwa Lee
Keyword(s):  
Finite Element ◽  
Contact Pressure ◽  
Bending Moment ◽  
Shear Loading ◽  
Transverse Load ◽  
Fe Model ◽  
Bolted Joint ◽  
Cyclic Bending ◽  
Second Stage ◽  
Cyclic Bending Moment

A three-dimensional finite element (FE) model with the consideration of the helix angle of the threads was developed to simulate the second stage self-loosening of a bolted joint. The second stage self-loosening refers to the graduate reduction in clamping force due to the back-off of the nut. The simulations were conducted for two plates jointed by a bolt and a nut and the joint was subjected to transverse or shear loading. An M12×1.75 bolt was used. The application of the preload was simulated by using an orthogonal temperature expansion method. FE simulations were conducted for several loading conditions with different preloads and relative displacements between the two clamped plates. It was found that due to the application of the cyclic transverse load, micro-slip occurred between the contacting surfaces of the engaged threads of the bolt and the nut. In addition, a cyclic bending moment was introduced on the bolted joint. The cyclic bending moment resulted in an oscillation of the contact pressure on the contacting surfaces of the engaged threads. The micro-slip between the engaged threads and the variation of the contact pressure were identified to be the major mechanisms responsible for the self-loosening of a bolted joint. Simplified finite element models were developed that confirmed the mechanisms discovered. The major self-loosening behavior of a bolted joint can be properly reproduced with the FE model developed. The results obtained agree quantitatively with the experimental observations.

Bending tests for the structural safety assessment of space truss members

2018 ◽  
Vol 33 (3-4) ◽  
pp. 138-149 ◽  
Author(s):  
Marco Bonopera ◽  
Kuo-Chun Chang ◽  
Chun-Chung Chen ◽  
Tzu-Kang Lin ◽  
Nerio Tullini
Keyword(s):  
Cross Sections ◽  
Flexural Rigidity ◽  
Compressive Force ◽  
Scale Space ◽  
Transverse Load ◽  
Structural Safety ◽  
Small Scale ◽  
Order Effects ◽  
Beam Columns ◽  
Space Truss

This article compares two nondestructive static methods used for the axial load assessment in prismatic beam-columns of space trusses. Examples include the struts and ties or the tension chords and diagonal braces of steel pipe racks or roof trusses. The first method requires knowledge of the beam-column’s flexural rigidity under investigation, whereas the second requires knowledge of the corresponding Euler buckling load. In both procedures, short-term flexural displacements must be measured at the given cross sections along the beam-column under examination and subjected to an additional transverse load. The proposed methods were verified by numerical and laboratory tests on beams of a small-scale space truss prototype made from aluminum alloy and rigid connections. In general, if the higher second-order effects are induced during testing and the corresponding total displacements are accurately measured, it would be easy to obtain tensile and compressive force estimations.

The Mathematical Analysis of Bow Girders of Any Shape

1956 ◽  
Vol 23 (4) ◽  
pp. 522-526
Author(s):  
M. M. Abbassi
Keyword(s):  
Mathematical Analysis ◽  
Concentrated Loads ◽  
Middle Point ◽  
Circular Arc ◽  
Distributed Load ◽  
Approximate Formulas

Abstract By using parametric equations in which the parameter is the angle included between the tangent at any point on the bow girder and the tangent at the middle point, the analysis of bow girders of shapes other than the circular arc can be treated mathematically. Exact and approximate formulas are given for symmetrical bow girders of any shape carrying a distributed load or two equal concentrated loads placed symmetrically with respect to the middle point of the girder.

scholarly journals An Investigation into the Effect of Cracking on the Response of Drilled and Postgrouted Concrete Pipe Pile under Lateral Loading

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zhijun Yang ◽  
Qing Fang ◽  
Bu Lv ◽  
Can Mei ◽  
Xudong Fu
Keyword(s):  
Flexural Rigidity ◽  
Bending Moment ◽  
Test Results ◽  
Lateral Loads ◽  
Analysis Method ◽  
Pile Head ◽  
Laterally Loaded Piles ◽  
Pipe Pile ◽  
Concrete Pipe ◽  
Laterally Loaded

The cracks are likely to initiate on a lateral loaded pile and would cause greater deflection at the pile head. However, there is a lack of thorough investigation into the effect of cracking on the response of the lateral loaded pile. In this article, a full-scale field test was carried out to investigate the behavior of Drilled and Postgrouted Concrete Pipe Pile under lateral loads. A novel analysis method for the lateral loaded pile, which can take the cracking effects into consideration, was proposed, and the validity was verified by the test results. With the proposed method, the cracking effects on flexural rigidity, displacement, rotation, and bending moment of the pile were studied. In brief, cracking effect would dramatically reduce the flexural rigidity of the pile, remarkable increase the displacement and rotation of the pile top, and slightly decrease bending moment of the pile. Unambiguously, the results show that the proposed method can excellently predict the response of laterally loaded piles under cracking effects.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

State of Stress of Castellated Beams with Circular Apertures under Distributed Load and Pure Bending

2019 ◽  
Vol 974 ◽  
pp. 521-528
Author(s):  
Alexej I. Pritykin
Keyword(s):  
Empirical Relation ◽  
Bending Moment ◽  
Empirical Dependence ◽  
Ansys Software ◽  
Pure Bending ◽  
Equivalent Stresses ◽  
Distributed Load ◽  
State Of Stress ◽  
Von Mises ◽  
Von Mises Stresses

The regularities of stress distribution in perforated beams with circular apertures under distributed load and pure bending. Such beams are made of different materials: carbon fiber is used in aircraft for these purposes, and steel is used in construction. Beams with different perforation parameters were considered and an empirical relation was obtained for equivalent von Mises stresses in castellated beams near the apertures’ outlines based on the analysis of FEM calculations. In this paper, beams made of C345 steel were considered. It is established that the maximum values ​​of equivalent stresses near apertures under different loading types vary along the beam length in proportion to the values ​​of the bending moment. The values ​​of stress concentration coefficients for the pure bending are determined depending on the perforation parameters. The acceptability of the obtained empirical dependencies for equivalent stresses was verified using the FEM calculations based on the ANSYS software package. There is a good correlation between the results of FEM calculations and empirical dependence.

scholarly journals Simulation of the Vibratory Behavior of Slender Shafts Subject to Transverse Loads Moving in the Axial Direction

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
F. Bucchi ◽  
P. Forte
Keyword(s):  
Mathematical Model ◽  
Manufacturing Industry ◽  
Axial Direction ◽  
Transverse Load ◽  
Design Phase ◽  
Vibration Level ◽  
Machine Performance ◽  
Transverse Loads ◽  
Spatial Interval ◽  
Influential Parameters

In various machines of the manufacturing industry, and in particular in paper converting machinery, there are shafts operating under conditions similar to that of a slender beam subjected to a transverse load moving in the axial direction. This condition can lead to vibrations and consequent deterioration of the machine performance and of the product quality. The problem has been theoretically studied in the literature since the 1990s. While shaft mass and stiffness are universally considered among the most influential parameters on its vibratory behavior, less obvious and not investigated in the literature is the influence of the spatial interval between two successive loads, an aspect that should be considered in the shaft design phase. In fact, if that is less than the length of the shaft, i.e., if there is more than one transverse load on the shaft at a given time, the vibration level may decrease with respect to the single-load configuration. This work describes the development of a mathematical model of a slender shaft hinged at its ends, representing the rotor of a paper roll perforating unit, with the SW Mathematica. The effect of a load moving axially at a given speed followed by similar loads after given spatial intervals was simulated investigating the influence of speed and load interval on shaft vibrations and resonance. The results showed how reducing the load interval can lead to a reduction of the shaft vibration which is a useful indication on possible design corrective actions.

Bending Athwart a Parallel-Stiffened Plate

1967 ◽  
Vol 34 (2) ◽  
pp. 278-282 ◽  
Author(s):  
N. J. Huffington
Keyword(s):  
Flexural Rigidity ◽  
Bending Moment ◽  
Plane Elasticity ◽  
Stiffened Plate ◽  
Theoretical Predictions ◽  
The Finite Difference Method ◽  
Approximate Procedure ◽  
Explicit Relation ◽  
Poisson Contraction

Consideration is given to the problem of predicting the flexural rigidity of plates reinforced by parallel, equally spaced stiffeners for the direction (in the plane of the plate) normal to the stiffener orientation, as well as the stresses induced by a bending moment acting in this direction. The determination of this lateral flexural rigidity is formulated in terms of a problem in plane elasticity which may be solved by the finite-difference method for specific cases. Results obtained by this method are compared with those obtained by a simpler approximate procedure. An explicit relation is derived for the flexural rigidity associated with Poisson contraction. Experimental results are introduced and compared with theoretical predictions.

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