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.

scholarly journals IV. On the practical solution of the most general problems in continuous beams

1879 ◽  
Vol 29 (196-199) ◽  
pp. 493-505
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
General Problem ◽  
Bending Moment ◽  
Moment Of Inertia ◽  
Shearing Stress ◽  
Practical Solution ◽  
Continuous Beams ◽  
The Moment

1. It is not necessary to enter into the question of the advisability of employing continuous girders in bridges with spans of less than 200 feet, but it is generally conceded that the increased economy due to the employment of continuous girders in longer spans more than counterbalances the well-known practical objections to continuity. Hence the practical solution of the general problem—given the conditions at the ends of a continuous girder, the spans, the moment of inertia of all cross sections, and the loading, to find the bending moment and shearing stress in every cross-section, is not unworthy of our attention.

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.

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.

Closed-form moment-curvature relations for reinforced concrete cross sections under bending moment and axial force

2016 ◽  
Vol 129 ◽  
pp. 67-80 ◽  
Author(s):  
Pedro Dias Simão ◽  
Helena Barros ◽  
Carla Costa Ferreira ◽  
Tatiana Marques
Keyword(s):  
Reinforced Concrete ◽  
Closed Form ◽  
Axial Force ◽  
Cross Sections ◽  
Bending Moment

The Behavior of Long Beams Under Impact Loading

1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust
Keyword(s):  
Plastic Deformation ◽  
Cross Sections ◽  
Constant Velocity ◽  
Bending Moment ◽  
Infinite Length ◽  
Longitudinal Impact ◽  
Deflection Curve ◽  
Transverse Impact ◽  
Cold Rolled ◽  
Annealed Copper

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.

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.

STIFFNESS OF REINFORCED CONCRETE STRUCTURES UNDER BENDING WITH TRANSVERSE AND LONGITUDINAL FORCES

2021 ◽  
Vol 98 (6) ◽  
pp. 5-19
Author(s):  
VL.I. KOLCHUNOV ◽  
◽  
O.I. AL-HASHIMI ◽  
M.V. PROTCHENKO ◽  
◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Cross Sections ◽  
Concrete Structures ◽  
Bending Moment ◽  
Reinforced Concrete Structures ◽  
The Matrix ◽  
Local Shear ◽  
The Difference ◽  
Inclined Cracks ◽  
Opening Width

The authors developed a model for single reinforced concrete strips in block wedge and arches between inclined cracks and approximated rectangular cross-sections using small squares in matrix elements. From the analysis of the works of N.I. Karpenko and S.N. Karpenko the "nagel" forces in the longitudinal tensile reinforcement and crack slip , as a function of the opening width and concrete deformations in relation to the cosine of the angle . The experimental " nagel " forces and crack slip dependences for the connection between and in the form of an exponent for the reinforcement deformations and spacing are determined. The forces have been calculated for two to three cross-sections (single composite strips) of reinforced concrete structures. On the bases of accepted hypothesis, a new effect of reinforced concrete and a joint modulus in a strip of composite single local shear zone for the difference of mean relative linear and angular deformations of mutual displacements of concrete (or reinforcement) are developed. The hypothesis allows one to reduce the order of the system of differential equations of Rzhanitsyn and to obtain in each joint the total angular deformations of concrete and the "nagel" effect of reinforcement. The curvature of the composite bars has a relationship from the total bending moment of the bars to the sum of the rigidities. The stiffness physical characteristics of the matrix from the compressed concrete area and the working reinforcement are obtained in a system of equations of equilibrium and deformation, as well as physical equations.

A shear center demonstration model using 3D-printing

2021 ◽  
pp. 030641902110574
Author(s):  
Lawrence N Virgin
Keyword(s):  
3D Printing ◽  
Cross Section ◽  
Cross Sections ◽  
Principal Axis ◽  
Practical Importance ◽  
Bending Moment ◽  
Shear Center ◽  
Cross Sectional ◽  
Thin Walls ◽  
Section Profile

Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment about a principal axis, results in uni-directional deflection, and no twisting. For example, in aerospace structures it is particularly important to assess the propensity of an airfoil section profile to resist bending and torsion under the action of aerodynamic forces. Cross-sections made of thin-walls, whether of open or closed form are of special practical importance and form the basis of the material in this paper. The advent of 3D-printing allows the development of tactile demonstration models based on non-trivial geometry and direct observation.

Performance of RC Precast Continuous Beams Incorporating New Strategy for Design and Allocating Connections

2020 ◽  
Vol 20 (06) ◽  
pp. 2040006
Author(s):  
Yingwu Zhou ◽  
Wenlong He ◽  
Biao Hu ◽  
Zhiheng Hu
Keyword(s):  
Bearing Capacity ◽  
Cross Sections ◽  
Bending Moment ◽  
Concrete Specimen ◽  
Steel Plates ◽  
Weak Point ◽  
Cross Section Area ◽  
New Strategy ◽  
Joint Connection ◽  
Column Joint

The performance of joint connections has always been the key to precast assembly structures. This paper proposes a new type of joint connection that is made by means of pre-embedded steel plates and connected by bolts or welding without any wet work. Located outside the beam-column joint, the connection is arranged around the inflection point of the beam where the bending moment is small. Three precast beams of different cross-sections and a set of cast-in-place concrete contrast beams were prepared and loaded by the anti-symmetric static loading method. The results show that the joint connection changes the failure mode of the specimens, transfers the failure section from the weak point to the non-weak point, and improves the bearing capacity of the specimens. With the increase of the cross-section area of the embedded steel plate at the joint, the bearing capacity and the ductility of the specimens increase. The energy consumption capacity of the precast specimen is significantly higher than that of the ordinary cast-in-place concrete specimen. Since the joint has not been destroyed, the component can be replaced when other parts of the specimen are destroyed.

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