Out-of-Plane Impact at the Tip of a Right-Angled Bent Cantilever Beam

1995 ◽  
Vol 62 (4) ◽  
pp. 887-892 ◽  
Author(s):  
B. Wang ◽  
T. X. Yu ◽  
S. R. Reid
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Bending Moment ◽  
Pure Bending ◽  
Concentrated Mass ◽  
Impulsive Load ◽  
Out Of Plane ◽  
History Of ◽  
The Cross

The present paper provides an analysis of the response of a right-angled bent cantilever beam subjected to an out-of-plane impulsive load (i.e., suddenly imposed velocity) applied to concentrated mass at its tip. If T0 and M0 are the fully plastic torque and bending moment, respectively, of the cross section, it is shown that for the case T0/M0 < 1, a double hinge mechanism is required, with a pure bending hinge in the first segment of the beam and a combined bending-torsion hinge in the second segment. The history of deformation is described following impartation of the load.

Part II. The Flattening of Monocoque Cylinders

1938 ◽  
Vol 42 (328) ◽  
pp. 302-319
Keyword(s):  
Variational Method ◽  
Potential Energy ◽  
Cross Section ◽  
Radial Displacement ◽  
Bending Moment ◽  
Experimental Investigations ◽  
Pure Bending ◽  
Centre Line ◽  
Thin Walled ◽  
The Cross

It is known from both theoretical and experimental investigations that St. Venant's assumption on the constancy of the shape of the cross section of girders in pure bending does not hold true in case of thin-walled sections. The greater flexibility than calculated according to ordinary bending theory of initially curved tubes, as experimentally found by Professor Bantlin, was perfectly explained by Professor von Kármán in 1911 on the assumption of a flattening of the section.In 1927 Brazier with the aid of the variational method determined exactly that the shape of an originally circular thin-walled bent cylinder corresponding to the least potential energy is quasi elliptical and that the cross section of the cylinder, therefore, must flatten, even if the centre line of the cylinder was originally straight. In consequence of the flattening St. Venant's linear law for the curvature loses its validity and the curvature increases more rapidly than the bending moment. For a certain value of the curvature the bending moment is a maximum, and after this value was reached the curvature increases even if the applied moment remains unchanged or decreases, fulfilling thereby the criterion of instability. This instability occurs when the rate of flattening, i.e., the maximum radial displacement of any point of the circumference of the tube divided by the original radius of the tube, will equal 2/9.

Piezoelectric T-Beam Microactuators

2008 ◽  
Author(s):  
Hareesh K. R. Kommepalli ◽  
Andrew D. Hirsh ◽  
Christopher D. Rahn ◽  
Srinivas A. Tadigadapa
Keyword(s):  
Cross Section ◽  
Fabrication Process ◽  
Mems Fabrication ◽  
Out Of Plane ◽  
Cantilevered Beam ◽  
Piezoelectric Mems ◽  
The Cross ◽  
T Beam ◽  
Cross Section Geometry

This paper introduces a novel T-beam actuator fabricated by a piezoelectric MEMS fabrication process. ICP-RIE etching from the front and back of a bulk PZT chip is used to produce stair stepped structures through the thickness with complex inplane shapes. Masked electrode deposition creates active and passive regions in the PZT structure. With a T-shaped crosssection, and bottom and top flange and web electrodes, a cantilevered beam can bend in-plane and out-of-plane with bimorph actuation in both directions. One of these T-beam actuators is fabricated and experimentally tested. An experimentally validated model predicts that the cross-section geometry can be optimized to produce higher displacement and blocking force.

scholarly journals The History of the Cross Section of Stock Returns

2016 ◽  
Author(s):  
Juhani T. Linnainmaa ◽  
Michael R. Roberts
Keyword(s):  
Stock Returns ◽  
Cross Section ◽  
History Of ◽  
The Cross

scholarly journals VII.—Rupture Stresses in Beams and Crane Hooks.

1914 ◽  
Vol 50 (1) ◽  
pp. 211-223
Author(s):  
Angus R. Fulton
Keyword(s):  
Compressive Stress ◽  
Cross Section ◽  
Bending Moment ◽  
Neutral Axis ◽  
Sectional Area ◽  
Inverse Proportion ◽  
Direct Loading ◽  
The Cross ◽  
External Forces ◽  
Distribution Of Stress

CONCLUSIONS1. It may be taken as conclusive that the final distribution of stress at rupture point in a member subjected to an external bending moment is a rectangular one, unless where the cohesion of adjacent layers is not sufficient to withstand the shear induced by the resisting moment of the section.2. That, provided shear does not take place, the neutral axis moves always to the position which reduces the summation of the tensile and compressive stress areas, across a section, to the equilibrant of the external forces. (In the case of a beam this reduces to zero; in that of a hook, at the principal section to the suspended weight.)3. That the total resisting moment of these stresses must be equal to the external bending moment as measured to the neutral axis at rupture point, but that these balancing moments do not differ materially from those measured to an axis obtained by dividing the sectional area into tensile and compressive stress areas which are in inverse proportion to the magnitude of their respective ultimate direct stresses.The advantage of these formulæ are important. It is possible to indicate with certainty the magnitude of the load which will cause rupture in a beam or a hook provided there is known the point of application or the effective arm of the load, the cross-section of the beam or hook, and the breaking strengths of the material when subjected to the different forms of direct loading.

scholarly journals Cross-Sectional Analysis of the Resistance of Rc Members Subjected to Bending With/without Axial Force

2021 ◽  
Author(s):  
Marek Lechman
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Equilibrium Equations ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Nonlinear Stress ◽  
The Cross ◽  
Sectional Analysis

The paper presents section models for analysis of the resistance of RC members subjected to bending moment with or without axial force. To determine the section resistance the nonlinear stress-strain relationship for concrete in compression is assumed, taking into account the concrete softening. It adequately describes the behavior of RC members up to failure. For the reinforcing steel linear elastic-ideal plastic model is applied. For the ring cross-section subjected to bending with axial force the normalized resistances are derived in the analytical form by integrating the cross-sectional equilibrium equations. They are presented in the form of interaction diagrams and compared with the results obtained by testing conducted on RC columns under eccentric compression. Furthermore, the ultimate normalized bending moment has been derived for the rectangular cross-section subjected to bending without axial force. It was applied in the cross-sectional analysis of steel and concrete composite beams, named BH beams, consisting of the RC rectangular core placed inside a reversed TT welded profile. The comparisons made indicated good agreements between the proposed section models and experimental results.

scholarly journals Limit analysis of beams under combined stresses

2008 ◽  
Vol 6 (1) ◽  
pp. 75-88 ◽  
Author(s):  
Marina Mijalkovic ◽  
Marina Trajkovic ◽  
Bojan Milosevic
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Shear Force ◽  
Pure Shear ◽  
Bending Moment ◽  
Beam Cross Section ◽  
Combined Stress ◽  
Pure Bending ◽  
Combined Stresses

The problem of the determination of limit bearing capacity of beam cross section under pure bending, eccentric tension, pure shear, as well as combined stress is considered in this paper. The influence functions of the bending moment and axial force, as well as the bending moment, axial and shear force on the cross section limit bearing capacity in case of rectangular and I beam cross section are derived.

scholarly journals The Ovalisation of Steel Circular Hollow Sections under Bending

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Manahel Sh. Khalaf ◽  
Amer M. Ibrahim
Keyword(s):  
Cross Section ◽  
Local Buckling ◽  
Bending Moment ◽  
Thickness Ratio ◽  
Experimental Results ◽  
Experimental Program ◽  
Specimen Length ◽  
Specimen Cross Section ◽  
The Cross

This paper investigates the ovalisation behavior of the Steel Circular Hollow Sections (CHSs) when subjected to bending moment. The experimental program included testing of ten specimens in four groups in order to examine the influence of changing the diameter, thickness, length and the presence of openings on the ovalisation phenomenon of these specimens.The experimental results showed that the ovalisation of the specimen cross-section appears clearly when the diameter to thickness ratio (D/t) is ranging from 17 to 50, while the ovalisation of the specimens that have D/t ratio greater than 50 is very little or unclear because the instability of these specimens are controlled by the local buckling. In addition, the change of the specimen length and the presence of openings didn’t cause the cross-section ovalisation

scholarly journals Study on ultimate strength of ship’s hull considering cross section and beam finite element.

2018 ◽  
Vol 177 ◽  
pp. 01030
Author(s):  
Muhammad Zubair Muis Alie ◽  
Juswan ◽  
Wahyuddin ◽  
Taufiqur Rachman
Keyword(s):  
Finite Element ◽  
Ultimate Strength ◽  
Cross Section ◽  
Bending Moment ◽  
Bulk Carrier ◽  
Longitudinal Bending ◽  
The Cross ◽  
The One ◽  
Double Hull ◽  
Oil Tanker

The objective of the present research is to study the ultimate strength of ship’s hull considering cross section and beam finite element under longitudinal bending. The single hull bulk carrier and double hull oil tanker are taken to be analysed. The one-frame space of ship is considered in the calculation. The cross section of ship’s hull is divided into element composed plate and stiffened plate. The cross section is assumed to be remained plane and the simply supported is imposed to both side of the cross section. The longitudinal bending moment is applied to the cross section for hogging and sagging condition. The Smith’s method is adopted and implemented into the in-house program of the cross section and beam finite element to calculate the ultimate strength of ship’s hull. The result of the ultimate strength for hogging and sagging condition obtained by considering the cross section and beam finite element is compared with one another.

THE INFLUENCE OF THE NUMBER AND POSITION OF DOWELS ON THE BENDING MOMENT CAPACITY OF HEAT-TREATED WOOD DOWEL JOINTS

2021 ◽  
Vol 14(63) (1) ◽  
pp. 67-76
Author(s):  
Bogdan I. BEDELEAN ◽  
Iosif NECULĂEȘ ◽  
Cosmin G. SPÎRCHEZ ◽  
Sergiu RĂCĂȘAN
Keyword(s):  
Cross Section ◽  
Treated Wood ◽  
Bending Moment ◽  
Moment Capacity ◽  
Moment Arms ◽  
Heat Treated ◽  
Wood Dowel ◽  
Ultimate Failure ◽  
The Cross ◽  
The Moment

In this work, the influence of the number of dowels and the option to place the dowels in the cross section of part on the bending moment capacity of heat-treated wood dowel joints was analysed. The joints, which were made of heat-treated ash, were tested by means of a universal testing machine.The ultimate failure load and the moment arms were used to figure out the bending moment capacity of the joints loaded in compression or in tension. The number of dowels affected the tensile strength of the L-shaped heat-treated wood joints. The modality to place the dowels in the cross section of rail, namely, in collinearity or in a triangular shape, did not significantly affect the strength of the heat-treated wood dowel joints.

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