Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 5, Problem 5.8.5P
Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued together to form a solid beam with dimensions 6.0 in. x 4.0 in. (sec figure). The beam is simply supported with a span of S ft.
- What is the maximum moment Mmaxthat may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft3.)
- Repeat part (a) if Mmaxis based on allowable bending stress of 2500 psi.
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The figure below shows two solid homogenous rectangular beam sections with (breadth x depth)
dimensions in two different orientations as follows:
Beam Section Orientation A (t mm x 2t mm); and
Beam Section Orientation B (2t mm x tmm).
Both beams sag when subjected to the same loading and support conditions resulting in
compressive stresses above the centroid line (neutral axis).
Which statement accurately describes the relative maximum compressive stress (ocompression)
between these beam section orientations?
O a.
O b.
Oc
tmm
2 mm
Beam Section Orientation A
2tmm
7 mm
Beam Section Orientation B
Maximum compressive stress (compression) in orientation B is greater than orientation A by
a factor of 2.
Maximum compressive stress (ocompression) in orientation A is greater than orientation B by
a factor of 4.
Maximum compressive stress (compression) in orientation B is greater than orientation A by
a factor of 4.
O d. Maximum compressive stress (ocompression) in orientation A is greater than…
The figure below shows two solid homogenous rectangular beam
sections with (breadth x depth) dimensions in two different
orientations as follows:
Beam Section Orientation A (t mm x 2t mm); and
Beam Section Orientation B (2t mm xt mm).
Both beams sag when subjected to the same loading and support
conditions resulting in compressive stresses above the centroid line
(neutral axis).
Which statement accurately describes the relative maximum
compressive stress (ocompression) between these beam section
orientations?
* Maximum compressive stress (acompression) in orientation A
is greater than orientation B by a factor of 4.
Maximum compressive stress (acompression) in orientation B
is greater than orientation A by a factor of 4.
* Maximum compressive stress (acompression) in orientation B
is greater than orientation A by a factor of 2.
4 Maximum compressive stress (acompression) in orientation A
is greater than orientation B by a factor of 2.
5.8-9 A laminated wood beam on simple sup-
ports (figure part a) is built up by gluing together four
2 in. X 4 in. boards (actual dimensions) to form a solid
beam 4 in. X 8 in. in cross section, as shown in the fig-
ure part b. The allowable shear stress in the glued joints
is 62 psi, the allowable shear stress in the wood is 175 psi,
and the allowable bending stress in the wood is 1650 psi.
(a) If the beam is 12 ft long, what is the allowable
load P acting at the one-third point along the
beam, as shown? (Include the effects of the
beam's own weight, assuming that the wood
weighs 35 lb/ft³.)
shutter
2 in.
L/3
2 in.
3 in.
2 in.
2 in.
3 in.
2 in.
(a)
4 in.
4 in.
(b)
(c)
PROBLEM 5.8-9
Chapter 5 Solutions
Mechanics of Materials (MindTap Course List)
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