A cantilever wooden beam of 2 m span is loaded with a uniformly distributed load of intensity 2kN/m over its entire length. The cross section of the beam is 80 mm wide and 120 mm deep with a semicircular grove of 20 mm radius as shown in Figure below. Calculate the following: a. Maximum tensile and compressive stresses in the section. b. The stresses at 1/4 of the dept from both the faces (Top and Bottom). c. Stress at mid- height of the section. d. Plot the stress variation diagram. e. Stress developed at the top, bottom and mid height of the sections, if the semicircular grove is removed from the section. f. Maximum tensile and compressive stresses, when the UDL load is replaced by concentrated load of 10 kN at its free end with the cross section remain same
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Bending of Beams
By Ansel C. Ugural and Saul K. Fenster
Aug 1, 2019
Contents
␡
5.1 Introduction
5.2 Pure Bending of Beams of Symmetrical Cross Section
5.3 Pure Bending of Beams of Asymmetrical Cross Section
5.4 Bending of A Cantilever of Narrow Section
5.5 Bending of a Simply Supported Narrow Beam
5.6 Elementary Theory of Bending
5.7 Normal and Shear Stresses
5.8 Effect of Transverse Normal Stress
5.9 Composite Beams
5.10 Shear Center
5.11 Statically Indeterminate Systems
5.12 Energy Method for Deflections
5.13 Elasticity Theory
5.14 Curved Beam Formula
5.15 Comparison of the Results of Various Theories
5.16 Combined Tangential and Normal Stresses
References
Problems
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Problems
Sections 5.1 through 5.5
5.1. A simply supported beam constructed of a 0.15 × 0.015 m angle is loaded by concentrated force P = 22.5 KN at its midspan (Fig. P5.1). Calculate stress σx at A and the orientation of the neutral axis. Neglect the effect of shear in bending and assume that beam twisting is prevented.
FIGURE P5.1
Explanation:
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