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Abstract
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Article Information:
Relative Error of the Mechanics of Material Solution on Simply Supported Beam under Uniform Load
Wen-jie Niu
Corresponding Author: Wen-jie Niu
Submitted: May 04, 2012
Accepted: June 08, 2012
Published: November 15, 2012 |
Abstract:
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The mechanics of material solution is a coarse analytical solution on the problem of simply
supported beam under uniform load. This paper intends to determine the relative error of the mechanics of
material solution. Solutions according to plane stress theory of elasticity theory are believed to be the true
solution. Results indicate that material mechanics solution σx seems applicable only when the ratio of beam
height to beam length is less than 0.1 and the ratio of distance between beam studied cross section and
midpoint in x direction to beam length is less than 0.49. When the ratio of beam height to beam length is
less than 0.1 and the ratio of distance between beam studied cross section and midpoint in x direction to
beam length is less than 0.49, maximum value of relative error for material mechanics solution σx is no
more than 12%. Material mechanics solution τxy is always correct for the problem of simply supported
beam under uniform load. Material mechanics solution σx is not applicable for the problem of simply
supported beam under uniform load.
Key words: Beam cross section coordinate in x direction, material mechanics solution, plane stress theory of theory of elasticity, ratio of beam height to beam length, relative error, ,
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Cite this Reference:
Wen-jie Niu, . Relative Error of the Mechanics of Material Solution on Simply Supported Beam under Uniform Load. Research Journal of Applied Sciences, Engineering and Technology, (22): 4830-4834.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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