This document contains Chapter 6 of the textbook "Mechanics of Materials, 5e" which discusses stresses in beams. It includes over 40 figures showing examples of composite beams, sandwich beams, stress and strain distributions in composite beams, reinforced concrete beams, and more. It also contains example problems related to analyzing stresses and determining reactions in different beam configurations.

1. Mechanics of Materials, 5e
Chapter 6
Stresses In Beams (Advanced Topics)

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Fig. 6-1 Examples of composite
beams: (a) bimetallic beam, (b)
plastic-coated steel pipe, and (c)
wood beam reinforced with a steel
plate.

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Fig. 6-2 Sandwich beams with: (a)
plastic core, (b) honeycomb core,
and (c) corrugated core.

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Fig. 6-3 (a) Composite
beam of two materials, (b)
cross section of beam, (c)
distributions of strains of ex
throughout the height of the
beam, and (d) distributions
of stresses sx in the beam
for the case where E 2 > E1.

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Fig. 6-4 Doubly symmetric cross section.

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Fig. 6-5 Cross
section of a
sandwich beam
having two axes of
symmetry (doubly
symmetric cross
section).

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Fig. 6-6 Reinforced concrete beam with longitudinal reinforcing bars
and vertical stirrups.

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Fig. 6-7 Example 6-1.
Cross section of a
composite beam of
wood and steel.

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Fig. 6-8 Example 6-2. Cross section of sandwich beam having
aluminum-alloy faces and a plastic core.

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Fig. 6-9 Composite beam
of two materials: (a) actual
cross section, and (b)
transformed section
consisting only of material
1.

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Fig. 6-10 Example 6-3. Composite beam of Example 6-1 analyzed by
the transformed-section method: (a) cross section of the original beam,
and (b) transformed section (material 1).

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Fig. 6-11 Beam with a lateral load acting as a plane of symmetry.

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Fig. 6-12 Doubly symmetric beam with an inclined load.

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Fig. 6-13 Sign conventions for bending moments My and M z.

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Fig. 6-14 Cross section of beam subjected to bending moments M y and M z.

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Fig. 6-15 Doubly
symmetric beam with
an inclined load P
acting at an angle q to
the positive y axis.

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Fig. 6-16 Example 6-4. Wood beam of rectangular cross section
serving as a roof purlin.

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Fig. 6-17 Solution to example 6-4. (a) components of the uniform
load, and (b) bending moments acting on a cross section.

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Fig. 6-18 Example 6-5. Cantilever beam with moment of inertia
1z much larger than 1y

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Fig. 6-19 Unsymmetric
beam subjected to a bending
moment M.

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Fig. 6-20 Sign
conventions for curvatures
ky and kz in the xy and xz
planes, respectively.

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Fig. 6-21 Bending moments M y and M z acting about the y and z
axes, respectively.

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Fig. 6-22 Unsymmetric cross section with the bending moment M
resolved into components M y and M z acting about the principal
centroidal axes.

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Fig. 6-23 Example 6-6. Channel section subjected to a bending
moment M acting at an angle q to the z axis.

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Fig. 6-24 Solution to Example 6-6.

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Fig. 6-25 Cantilever beam
with singly symmetric cross
section: (a) beam with load,
and (b) intermediate cross
section of beam showing stress
resultants P and Mo, centroid
C, and shear center S.

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Fig. 6-26 Singly symmetric beam with load P applied at point A.

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Fig. 6-27 (a) Doubly symmetric beam
with a load P acting through the
centroid (and shear center), and (b)
singly symmetric beam with a load P
acting through the shear center.

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Fig. 6-28 Unsymmetric beam
with a load P acting through the
shear center S.

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Fig. 6-29 Typical beams of thin-walled open cross section (wide-
flange beam or I-beam, channel beam, angle section, Z-section, and T-
beam).

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Fig. 6-30 Shear stresses in a beam of thin-walled open cross
section. (the y and z axes are principal centroidal axes).

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Fig. 6-31 Shear stresses in a wide-flange beam.

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Fig. 6-32 Shear center S of a channel section.

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Fig. 6-33 Shear center of an equal-leg angle section

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Fig. 6-34 Shear centers of sections consisting of two intersecting
narrow rectangles.

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Fig. 6-35 Shear center of a thin-walled Z-section.

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Fig. 6-36 Example 6-7. Shear center of a thin-walled semicircular section.

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Fig. 6-37 Idealized stress-strain diagram for an elastoplastic material.

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Fig. 5-38 Beam of elastoplastic material subjected to a positive bending
moment M.

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Fig. 6-39 Stress distributions in a beam of elastoplastic material.

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Fig. 6-40 Location of the neutral axis and determination of the plastic
moment Mp under fully plastic conditions.

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Fig. 6-41 Rectangular cross section.

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Fig. 6-42 Stress distribution in a beam of rectangular cross section
with an elastic core ( My  M  Mp ).

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Fig. 6-43 Cross section of a wide-flange beam.

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Fig. 6-44 Example 6-8. Cross section of a circular beam (elastoplastic
material).

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Fig. 6-45 Solution to Example 6-8.

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Fig. 6-46 Example 6-9. Cross
section of a hollow box beam
(elastoplastic material).

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Fig. 6-47 Solution to Example 6-9.

49. Chapter 6
Problems

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Problem 6.2-1

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Problem 6.2-2

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Problem 6.2-3

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Problem 6.2-4

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Problem 6.2-5

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Problem 6.2-6

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Problem 6.2-7 and 6.2-8

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Problem 6.2-9

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Problem 6.2-10

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Problem 6.3-1

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Problem 6.3-2

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Problem 6.3-3

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Problem 6.3-4

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Problem 6.3-5 and 6.3-6

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Problem 6.3-7

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Problem 6.3-8

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Problem 6.3-9

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Problem 6.3-10

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Problem 6.3-11

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Problem 6.3-12

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Problem 6.3-13

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Problem 6.4-1

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Problem 6.4-2 and 6.4-3

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Problem 6.4-4 and 6.4-5

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Problem 6.4-6 and 6.4-7

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Problem 6.4-8

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Problem 6.4-9 and 6.4-10

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Problem 6.4-11

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Problem 6.5-1 and 6.5-2

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Problem 6.5-3 and 6.5-4

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Problem 6.5-5

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Problem 6.8-1 and 6.8-2

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Problem 6.8-3 and 6.8-4

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Problem 6.9-1 and 6.9-2

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Problem 6.9-3

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Problem 6.9-4

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Problem 6.9-5

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Problem 6.9-6

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Problem 6.9-7

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Problem 6.9-8

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Problem 6.9-9

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Problem 6.9-10

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Problem 6.9-11

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Problem 6.9-12

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Problem 6.10-1

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Problem 6.10-2

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Problem 6.10-3

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Problem 6.10-4

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Problem 6.10-5 and 6.10-6

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Problem 6.10-11 and 6.10-12

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Problem 6.10-13 through 6.10-16

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Problem 6.10-19 and 6.10-20

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Problem 6.10-21

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Problem 6.10-22