An Improved Method for Calculating Bending Moment and Shearing Force of Beam in Numerical Modelling

This paper takes a sluice reconstruction project as an example. The constraint internal force, the related axis force, bending moment, and shearing force at the corresponding section are solved according to the unit stress and internal force balance. Furthermore, technology of mesh auto-generation in cross-section is utilized to plot the internal force graph of the structure directly, which will provide reference for reinforcement design and make it more convenient.

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Macaulay's Method for a Timoshenko Beam

International Journal of Mechanical Engineering Education ◽

10.7227/ijmee.35.4.3 ◽

2007 ◽

Vol 35 (4) ◽

pp. 285-292 ◽

Cited By ~ 9

Author(s):

N. G. Stephen

Keyword(s):

Timoshenko Beam ◽

Bending Moment ◽

Shearing Force ◽

Bernoulli Beam ◽

Deflection Curve ◽

Axial Coordinate ◽

Deflection Analysis ◽

Euler Bernoulli Beam

The Macaulay bracket notation is familiar to many engineers for the deflection analysis of a Euler–Bernoulli beam subject to multiple or discontinuous loads. An expression for the internal bending moment, and hence curvature, is valid at all locations along the beam, and the deflection curve can be calculated by integrating twice with respect to the axial coordinate. The notation obviates the need for matching of multiple constants of integration for the various sections of the beam. Here, the method is extended to a Timoshenko beam, which includes the additional deflection due to shear. This requires an additional expression for the shearing force, also valid at all locations along the beam.

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Large Sideward Deflections of Two-Hinged Circular Arches

Journal of Engineering for Industry ◽

10.1115/1.3428073 ◽

1971 ◽

Vol 93 (4) ◽

pp. 1268-1274 ◽

Cited By ~ 1

Author(s):

Donald A. Dadeppo ◽

Robert Schmidt

Keyword(s):

Applied Load ◽

Normal Force ◽

Bending Moment ◽

Point Load ◽

Elliptic Integrals ◽

Graphical Form ◽

Shearing Force ◽

Underlying Theory

Deflections and stress resultants are calculated for hinged-hinged circular arches subjected to a horizontal point load at the crown. The underlying theory is based on the Bernoulli-Euler hypothesis. The magnitudes of deflections are unrestricted. The solutions are expressed in terms of Legendre’s elliptic integrals of the first and second kind. Calculated results are presented in graphical form. These include deflected configurations and load-deflection curves, as well as normal force, shearing force, and bending moment diagrams for arches with three different subtending angles and three different values of the applied load on each arch.

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Proof of a Fundamental Relation in the Theory of Bending between the Bending Moment and Load Curves, or between the Deflection and Bending Moment Curves

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500033976 ◽

1911 ◽

Vol 30 ◽

pp. 64-64

Author(s):

E. M. Horsburgh

Keyword(s):

Bending Moment ◽

Vertical Line ◽

Fundamental Relation ◽

Shearing Force ◽

Usual Convention

The important relation in the Theory of Bending between the curves of Bending Moment (B.M.), Shearing Force (S.F.), and Load, or between those of Deflection, Slope, and Bending Moment, viz., that the tangents to the first of either set intersect in a vertical line through the centroid of the corresponding area of the last, under the usual convention of drawing, is usually not proved in Engineering Treatises, or else is established in simple cases by the polygon of loads.

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Quantifying lahar damage using numerical modelling

10.5194/nhess-2016-282 ◽

2016 ◽

Author(s):

Stuart R. Mead ◽

Christina Magill ◽

Vincent Lemiale ◽

Jean-Claude Thouret ◽

Mahesh Prakash

Keyword(s):

Numerical Modelling ◽

Critical Infrastructure ◽

Human Life ◽

Bending Moment ◽

Building Damage ◽

Minor Role ◽

Building Vulnerability ◽

Hazard Exposure ◽

Inundation Area

Abstract. Lahars are volcanic flows containing a mixture of fluid and sediment that have caused significant damage to buildings, critical infrastructure and human life. The extent of this damage is controlled by properties of the lahar, location of elements at risk and susceptibility of these elements to the lahar. Here we focus on understanding lahar-induced building damage. Quantification of building damage can be difficult due to the complexity of lahar behaviour (hazard), uncertainty in number and type of buildings exposed to the lahar (exposure) and the uncertain susceptibility of buildings to lahar induced damage (vulnerability). In this paper, we quantify and examine the relative importance of lahar hazard, exposure and vulnerability in determining building damage with reference to a case study in the city of Arequipa, Peru. Numerical modelling is used to investigate lahar properties important in determining the inundation area and forces applied to buildings. Building vulnerability is quantified through the development of critical depth–pressure curves based on the ultimate bending moment of masonry structures. In the case study area, results suggest that building strength plays a minor role in determining overall building losses in comparison to the effects of building exposure and lahar hazard properties such as hydraulic characteristics of the flow.

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