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 9, Problem 9.7.10P
A tapered cantilever beam AB supports a concentrated load P at the free end (see figure). The cross sections of the beam are rectangular tubes with constant width b, outer Tube depth dAat A, and outer tube depth dB— ldA/2 at support B. The tube thickness is constant, as t = dA/20. IAis the moment of inertia of the outer tube at end A of the beam.
If the moment of inertia of the tube is approximated as la{x) as defined, find the equation of the deflection curve and the deflection 5^ at the free end of the beam due to the load P.
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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 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.
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…
H.W: Find the Values of the shear stress at point A, B,
and C in the beam Cross- Sedion shown in the figure
below when subjeded to a shaurr forced @= loo kw. Hence
Sketch the shear stress distribution dingram.
A
B
R2
25 mm
R= 50 mm
Rzs75 mm
Chapter 9 Solutions
Mechanics of Materials (MindTap Course List)
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