Mechanics of Materials 6th. Edition by James M. Gere | 9780534417932 | 0534417930

Mechanics of Materials

132 SOLVED PROBLEMS

8 SOLVED PROBLEMS

Question: 5.7

A simple beam AB of span length 21 ft must support a uniform load q = 2000 lb/ft distributed along the beam in the manner shown in Fig. 5-21a. Considering both the uniform load and the weight of the beam, and also using an allowable bending stress of 18,000 psi, select a structural steel beam of ...

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In this example we will proceed as follows: (1) Fi...

Question: 11.1

A long, slender column ABC is pin-supported at the ends and compressed by an axial load P (Fig. 11-14). Lateral support is provided at the midpoint B in the plane of the figure. However, lateral support perpendicular to the plane of the figure is provided only at the ends. The column is constructed ...

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Because of the manner in which it is supported, th...

Question: 6.6

A channel section (C 10 × 15.3) is subjected to a bending moment M = 15 k-in. oriented at an angle θ = 10° to the z axis (Fig. 6-23). Calculate the bending stresses σA and σB at points A and B, respectively, and determine the position of the neutral axis. ...

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Properties of the cross section. The centroid C is...

Question: 6.5

A 12-foot long cantilever beam (Fig. 6-18a) is constructed from an S 24 × 80 section (see Table E-2 of Appendix E for the dimensions and properties of this beam). A load P = 10 k acts in the vertical direction at the end of the beam. Because the beam is very narrow compared to its height ...

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(a) Maximum bending stresses when the load is alig...

Question: 5.5

A simply supported wood beam having a span length L = 12 ft carries a uniform load q = 420 lb/ft (Fig. 5-19). The allowable bending stress is 1800 psi, the wood weighs 35 lb/ft³, and the beam is supported laterally against sideways buckling and tipping. Select a suitable size for the beam from the ...

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Since we do not know in advance how much the beam ...

Question: 12.5

Determine the moment of inertia Ic with respect to the horizontal axis C-C through the centroid C of the beam cross section shown in Fig. 12-16. (The position of the centroid C was determined previously in Example 12-2 of Section 12.3.) Note: From beam theory (Chapter 5), we know that axis C-C is ...

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We will determine the moment of inertia

I_{...

Question: 12.2

The cross section of a steel beam is constructed of a W 18 × 71 wide-flange section with a 6 in. × 1/2 in. cover plate welded to the top flange and a C 10 × 30 channel section welded to the bottom flange (Fig. 12-8). Locate the centroid C of the cross-sectional area. ...

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Let us denote the areas of the cover plate, the wi...

Question: 11.8

A wood post of rectangular cross section (Fig. 11-40) is constructed of Douglas fir lumber having a compressive design stress Fc = 11 MPa and modulus of elasticity E = 13 GPa. The length of the post is L and the cross-sectional dimensions are b and h. The supports at the ends of the post provide ...

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(a) Allowable axial load. The allowable load (from...

Question: 11.5

A steel column is constructed from a W 10 × 60 wide-flange section (Fig. 11-37). Assume that the column has pin supports and may buckle in any direction. Also, assume that the steel has modulus of elasticity E = 29,000 ksi and yield stress σY = 36 ksi. (a) If the length of the column is L = 20 ft, ...

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We will use the AISC formulas (Eqs. 11-79 through ...

Question: 9.9

A simple beam AB of span length L has an overhang BC of length a (Fig. 9-21a). The beam supports a uniform load of intensity q throughout its length. Obtain a formula for the deflection δC at the end of the overhang (Fig. 9-21c). (Note: The beam has constant flexural rigidity EI.) ...

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We can find the deflection of point C by imagining...

Question: 9.12

A simple beam ADB supports a concentrated load P acting at the position shown in Fig. 9-26. Determine the angle of rotation θA at support A and the deflection δD under the load P. Note: The beam has a length L and constant flexural rigidity EI. ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 10.6

A beam ABC (Fig. 10-19a) rests on simple supports at points A and B and is supported by a cable at point C. The beam has total length 2L and supports a uniform load of intensity q. Prior to the application of the uniform load, there is no force in the cable nor is there any slack in the cable. When ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 11.7

An aluminum tube (alloy 2014-T6) with an effective length L = 16.0 in. is compressed by an axial force P = 5.0 k (Fig. 11-39). Determine the minimum required outer diameter d if the thickness t equals one-tenth the outer diameter. ...

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We will use the Aluminum Association formulas for ...

Question: 10.4

A fixed-end beam AB (Fig. 10-15a) is loaded by a force P acting at an intermediate point D. Find the reactive forces and moments at the ends of the beam using the method of superposition. Also, determine the deflection at point D where the load is applied. ...

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This beam has four unknown reactions (a force and ...

Question: 10.3

A two-span continuous beam ABC supports a uniform load of intensity q, as shown in Fig. 10-14a. Each span of the beam has length L. Using the method of superposition, determine all reactions for this beam. ...

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This beam has three unknown reactions (

R_A,...

Question: 9.7

A cantilever beam AB with a uniform load of intensity q acting on the right-hand half of the beam is shown in Fig. 9-19a. Obtain formulas for the deflection δB and angle of rotation θB at the free end (Fig. 9-19c). (Note: The beam has length L and constant flexural rigidity EI.) ...

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In this example we will determine the deflection a...

Question: 9.13

A beam ABCDE on simple supports is constructed from a wide-flange beam by welding cover plates over the middle half of the beam (Fig. 9-28a). The effect of the cover plates is to double the moment of inertia (Fig. 9-28b). A concentrated load P acts at the midpoint C of the beam. Determine the ...

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Differential equations of the deflection curve. In...

Question: 7.7

An element of material in plane strain undergoes the following strains: εx = 340 × 10^-6 εy = 110 × 10^-6 γxy = 180 × 10^-6 These strains are shown highly exaggerated in Fig. 7-36a, which shows the deformations of an element of unit dimensions. Since the edges of the element have unit lengths, the ...

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(a) Element oriented at an angle θ = 30°. The stra...