A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter d x are bonded to form a composite beam, as shown in the figure, (a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7 T i in the titanium and an allowable stress ( u in the copper (Assume that the moduli of elasticity for the titanium and copper are E r - and £ C u , respectively.) (b) If d 1 = 40 mm, d { = 36 mm, E T l = 120 GPa, E C u = 110 GPa, o- T i = 840 MPa, and ctqj = 700 MPa, what is the maximum bending moment Ml (c) What new value of copper diameter d t will result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allow- able stress values at the same time).

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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
BuyFind

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

Solutions

Chapter
Section
Chapter 6, Problem 6.2.6P
Textbook Problem

A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure,

(a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress ( u in the

copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.)

(b)

If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and

ctqj = 700 MPa, what is the maximum bending moment Ml (c)

What new value of copper diameter dtwill result

in a balanced design? (i.e., a balanced design is

that in which titanium and copper reach allow-

able stress values at the same time).

  Chapter 6, Problem 6.2.6P, A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded

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Chapter 6 Solutions

Mechanics of Materials (MindTap Course List)
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 - Solve the preceding problem for a W 250 x 89...Ch. 6 - Determine the yield moment MY, plastic moment MP,...Ch. 6 - Solve t he p receding problem for a W 410 × 85...Ch. 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 - .16 Solve the preceding problem for a box beam...Ch. 6 - AW 10º 60 wide-flange b earn is subjected to a...Ch. 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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