Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
9th Edition
ISBN: 9781337594318
Author: Barry J. Goodno; James M. Gere
Publisher: Cengage Learning
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Chapter 6, Problem 6.10.1P
Determine the shape factor f for a cross section in the shape of a double trapezoid having the dimensions shown in the figure.
Also, check your result for the special cases of a rhombus (b1= 0) and a rectangle (b1= b2).
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3) For the given plate subjected to two point forces,
calculate the nodal displacements and the moments at points A and B. (Note that A is the mid-point of
the finite element)
E = 30000 MPa
h = 0.14 m
v = 0.20
2 m
2 m
50 kN
2 m
50 kN
A
B
50 kN
50 kN
2 m
50
Cross-section along
the symmetry axis
The dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C.
What is the reaction force at A? Let a positive reaction force be to the right.
The cantilever beam depicted below is rigidly attached to a wall at point A, which coincides with the
coordinate system's origin. Point B near the beam's free end has coordinates (1.3, 0.3, 2.4) m. The vector
r₁ = 11+12ĵ+1km is perpendicular to the beam axis AB and oriented parallel to the width dimension of
the cross-section, as shown. The vector 7₂ = 29.1î+1.23 — 14.72 m is perpendicular to the beam axis AB
and r₁. The force P applied to point B of the beam has the direction angles 0 = 144°, 0y = 72°,0₂ = 60°.
fa
Questions:
a Assuming |P| = 1000 N Compute the force moment about ri and 72.
b Previous experiments on similar beams made of the same material have shown that the beam will
rupture and be torn from the wall when the absolute value of the moment of P about r₁ is 4000 Nm,
or when the absolute value of the moment of P about r2 is 6000 Nm. Determine the magnitude of
P that will cause this beam to fail.
Chapter 6 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
Ch. 6 - A composite beam is constructed using a steel...Ch. 6 - A wood beam is strengthened using two steel plates...Ch. 6 - A composite beam consisting of fiberglass faces...Ch. 6 - A wood beam with cross-sectional dimensions 200 mm...Ch. 6 - A hollow box beam is constructed with webs of...Ch. 6 - A r o lukI f/frm f «m t ub e of ou t sid e d ia...Ch. 6 - A beam with a guided support and 10-ft span...Ch. 6 - A plastic-lined steel pipe has the cross-sectional...Ch. 6 - The cross section of a sand wie h beam consisting...Ch. 6 - The cross section of a sandwich beam consisting of...
Ch. 6 - A bimetallic beam used in a temperature-control...Ch. 6 - A simply supported composite beam 3 m long carries...Ch. 6 - A simply supported wooden I-beam with a 12-ft span...Ch. 6 - -14 A simply supported composite beam with a 3.6 m...Ch. 6 - -15 A composite beam is constructed froma wood...Ch. 6 - A wood beam in a historic theater is reinforced...Ch. 6 - Repeat Problem 6.2-1 but now assume that the steel...Ch. 6 - Repeat Problem 6.2-17 but now use a...Ch. 6 - A sandwich beam having steel faces enclosing a...Ch. 6 - A wood beam 8 in. wide and 12 in. deep (nominal...Ch. 6 - A simple beam of span length 3.2 m carries a...Ch. 6 - A simple beam that is 18 ft long supports a...Ch. 6 - The composite beam shown in the figure is simply...Ch. 6 - The cross section of a beam made of thin strips of...Ch. 6 - Consider the preceding problem if the beam has...Ch. 6 - A simple beam thai is IS ft long supports a...Ch. 6 - The cross section of a composite beam made of...Ch. 6 - A beam is constructed of two angle sections, each...Ch. 6 - The cross section of a bimetallic strip is shown...Ch. 6 - A W 12 x 50 steel wide-flange beam and a segment...Ch. 6 - A reinforced concrete beam (see figure) is acted...Ch. 6 - A reinforced concrete T-beam (see figure) is acted...Ch. 6 - A reinforced concrete slab (see figure) is...Ch. 6 - A wood beam reinforced using two channels is...Ch. 6 - A wood beam reinforced by an aluminum channel...Ch. 6 - A beam with a rectangular cross section supports...Ch. 6 - A wood beam with a rectangular cross section (see...Ch. 6 - Solve the preceding problem for the following...Ch. 6 - A simply supported wide-flange beam of span length...Ch. 6 - Solve the preceding problem using the fol...Ch. 6 - A wood cantilever beam with a rectangular cross...Ch. 6 - Solve the preceding problem for a cantilever beam...Ch. 6 - A 2-m-long cantilever beam is constructed using a...Ch. 6 - A wood beam AB with a rectangular cross section (4...Ch. 6 - A steel beam of I-section (see figure) is simply...Ch. 6 - A cantilever beam with a wide-flange cross section...Ch. 6 - Solve the preceding problem using a W 310 x 129...Ch. 6 - A cantilever beam of W 12 × 14 section and length...Ch. 6 - A cantilever beam built up from two channel...Ch. 6 - A built-Lip I-section steel beam with channels...Ch. 6 - Repeat Problem 6.4-14 but use the configuration of...Ch. 6 - A beam with a channel section is subjected to a...Ch. 6 - A beam with a channel section is subjected to a...Ch. 6 - An angle section with equal legs is subjected to a...Ch. 6 - An angle section with equal legs is subjected to a...Ch. 6 - A beam made up all woun equal leg angles is...Ch. 6 - The Z-section of Example D-7 is subjected to M = 5...Ch. 6 - The cross section of a steel beam is constructed...Ch. 6 - The cross section of a steel beam is shown in the...Ch. 6 - A beam with a semicircular cross section of radius...Ch. 6 - .10 A built-up bourn supporting a condominium...Ch. 6 - Asteelpost (E = 30 × 106 psi) having thickness t =...Ch. 6 - A C 200 x 17.1 channel section has an angle with...Ch. 6 - A cold-formed steel section is made by folding a...Ch. 6 - A simple beam with a W 10 x 30 wide-flange cross...Ch. 6 - Solve the preceding problem for a W 250 × 44.8...Ch. 6 - A beam of wide-flange shape, W 8 x 28, has the...Ch. 6 - Solve the preceding problem for a W 200 × 41,7...Ch. 6 - Calculate the distance e from the cent crime of...Ch. 6 - Calculate the distance e from the centerline of...Ch. 6 - The cross section of an unbalanced wide-flange...Ch. 6 - The cross section of an unbalanced wide-flange...Ch. 6 - The cross section of a channel beam with double...Ch. 6 - The cross section of a slit circular tube of...Ch. 6 - The cross section of a slit square tube of...Ch. 6 - The cross section of a slit rectangular tube of...Ch. 6 - A U-shaped cross section of constant thickness is...Ch. 6 - Derive the following formula for the distance e...Ch. 6 - Derive the following formula for the distance e...Ch. 6 - The cross section of a sign post of constant...Ch. 6 - A cross section in the shape of a circular arc of...Ch. 6 - Determine the shape factor f for a cross section...Ch. 6 - (a) Determine the shape factor/for a hollow...Ch. 6 - A propped cantilever beam of length L = 54 in....Ch. 6 - A steel beam of rectangular cross section is 40 mm...Ch. 6 - .5 Calculate the shape factor j for the...Ch. 6 - Solve the preceding problem for a wide-flange beam...Ch. 6 - Determine the plastic modulus Z and shape...Ch. 6 - Prob. 6.10.8PCh. 6 - Prob. 6.10.9PCh. 6 - Prob. 6.10.10PCh. 6 - A hollow box beam with height h = 16 in,, width h...Ch. 6 - Solve the preceding problem for a box beam with...Ch. 6 - A hollow box beam with height h = 9.5 in., inside...Ch. 6 - Solve the preceding problem for a box beam with...Ch. 6 - The hollow box beam shown in the figure is...Ch. 6 - Prob. 6.10.16PCh. 6 - Prob. 6.10.17PCh. 6 - A singly symmetric beam with a T-section (see...Ch. 6 - A wide-flange beam with an unbalanced cross...Ch. 6 - .20 Determine the plastic moment Mpfor beam having...
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