To Solve the Load of Beam by Shearing Force Diagram and Bending Moment Diagram??"Reverse Thinking in Strength of Materials

The paper has a discussion of forward problem and inverse problem for beams in strength of materials. Known load case of a beam can certainly determine its shearing force diagram and bending moment diagram, but conversely, there may be a variety of statically determinate or statically indeterminate constraint conditions. Furthermore, the solution from statically indeterminate constraint conditions doesnt agree with the given shearing force diagram and bending moment diagram in a general way.

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Shearing force and bending moment

Mechanical Technology ◽

10.1016/b978-0-434-90078-7.50005-7 ◽

1990 ◽

pp. 10-20

Author(s):

D.H. Bacon ◽

R.C. Stephens

Keyword(s):

Bending Moment ◽

Shearing Force

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Probabilistic Analysis of Plastic Collapse of Plane Frame Structure under Combined Effect of Bending Moment, Shearing Force and Axial Force

Journal of the Society of Naval Architects of Japan ◽

10.2534/jjasnaoe1968.1985.158_310 ◽

1985 ◽

Vol 1985 (158) ◽

pp. 310-318

Author(s):

Hiroo Okada ◽

Yoshisada Murotsu ◽

Satoshi Matsuzaki ◽

Shinji Katsura

Keyword(s):

Axial Force ◽

Probabilistic Analysis ◽

Bending Moment ◽

Combined Effect ◽

Frame Structure ◽

Plastic Collapse ◽

Shearing Force ◽

Plane Frame

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The Study of FEM for Internal Force Analysis of the Sluice Structure

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.71-78.3275 ◽

2011 ◽

Vol 71-78 ◽

pp. 3275-3279

Author(s):

Xiao Na Li ◽

Tong Chun Li ◽

Yuan Ding

Keyword(s):

Cross Section ◽

Bending Moment ◽

Internal Force ◽

Force Balance ◽

Shearing Force ◽

Force Analysis ◽

Reconstruction Project ◽

Unit Stress ◽

Reinforcement Design

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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