Mechanics of Materials 4th. Edition by James M. Gere, Stephen P. Timoshenko. | 9780534934293 | 534951023

Mechanics of Materials

13 SOLVED PROBLEMS

130 SOLVED PROBLEMS

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: 11.4

A steel wide-flange column of W 14 × 82 shape (Fig. 11-28a) is pin-supported at the ends and has a length of 25 ft. The column supports a centrally applied load P1 = 320 k and an eccentrically applied load P2 = 40 k (Fig. 11-28b). Bending takes place about axis 1-1 of the cross section, and the ...

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(a) Maximum compressive stress. The two loads [lat...

Question: 9.5

A simple beam AB with an overhang BC supports a concentrated load P at the end of the overhang (Fig. 9-15a). The main span of the beam has length L and the overhang has length L/2. Determine the equations of the deflection curve and the deflection δC at the end of the overhang (Fig. 9-15b). Use the ...

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Differential equations of the deflection curve. Be...

Question: 8.7

A tubular post of square cross section supports a horizontal platform (Fig. 8-28). The tube has outer dimension b = 6 in. and wall thickness t = 0.5 in. The platform has dimensions 6.75 in. × 24.0 in. and supports a uniformly distributed load of 20 psi acting over its upper surface. The resultant ...

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Stress resultants. The force

P_{1}

...

Question: 8.6

A sign of dimensions 2.0 m × 1.2 m is supported by a hollow circular pole having outer diameter 220 mm and inner diameter 180 mm (Fig. 8-26). The sign is offset 0.5 m from the centerline of the pole and its lower edge is 6.0 m above the ground. Determine the principal stresses and maximum shear ...

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Stress resultants. The wind pressure against the s...

Question: 8.3

A simple beam AB with span length L = 6 ft supports a concentrated load P = 10,800 lb acting at distance c = 2 ft from the right-hand support (Fig. 8-17). The beam is made of steel and has a rectangular cross section of width b = 2 in. and height h = 6 in. Investigate the principal stresses and ...

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We begin by using the flexure and shear formulas t...

Question: 7.8

A 45° strain rosette (also called a rectangular rosette) consists of three electrical-resistance strain gages arranged to measure strains in two perpendicular directions and also at a 45° angle between them, as shown in Fig. 7-37a. The rosette is bonded to the surface of the structure before it is ...

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At the surface of the stressed object, the materia...

Question: 5.17

A tubular beam ACB of length L = 60 in. is pin-supported at its ends and loaded by an inclined force P at midlength (Fig. 5-47a). The distance from the point of application of the load P to the longitudinal axis of the tube is d = 5.5 in. The cross section of the tube is square (Fig. 5-47b) with ...

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Beam and loading. We begin by representing the bea...

Question: 6.1

A composite beam (Fig. 6-7) is constructed from a wood beam (4.0 in. × 6.0 in. actual dimensions) and a steel reinforcing plate (4.0 in. wide and 0.5 in. thick). The wood and steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M = 60 k-in. ...

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Neutral axis. The first step in the analysis is to...

Question: 10.1

A propped cantilever beam AB of length L supports a uniform load of intensity q (Fig. 10-6). Analyze this beam by solving the second-order differential equation of the deflection curve (the bending-moment equation). Determine the reactions, shear forces, bending moments, slopes, and deflections of ...

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Because the load on this beam acts in the vertical...

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: 12.8

Determine the orientations of the principal centroidal axes and the magnitudes of the principal centroidal moments of inertia for the cross-sectional area of the Z-section shown in Fig. 12-29. Use the following numerical data: height h = 200 mm, width b = 90 mm, and thickness t = 15 mm. ...

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Let us use the xy axes (Fig. 12-29) as the referen...

Question: 12.7

Determine the product of inertia Ixy of the Z-section shown in Fig. 12-24. The section has width b, height h, and thickness t. ...

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To obtain the product of inertia with respect to t...

Question: 12.6

A right triangle with base b and height h is shown in Fig. 12-23. (a) Determine the product of inertia Ixy with respect to the xy axes having their origin O at the 90° vertex of the triangle, (b) Determine the product of inertia Ixcyc with respect to the centroidal axes xcyc. ...

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(a) Product of inertia with respect to the xy axes...

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_c...

Question: 12.4

The parabolic semisegment OAB shown in Fig. 12-15 has base b and height h. Using the parallel-axis theorem, determine the moments of inertia Ixc and Iyc with respect to the centroidal axes xc and yc. ...

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We can use the parallel-axis theorem (rather than ...

Question: 12.3

Determine the moments of inertia Ix and Iy for the parabolic semisegment OAB shown in Fig. 12-12. The equation of the parabolic boundary is y = f(x) = h(1 – x²/b²) (e) (This same area was considered previously in Example 12-1.) ...

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To determine the moments of inertia by integration...

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: 12.1

A parabolic semisegment OAB is bounded by the x axis, the y axis, and a parabolic curve having its vertex at A (Fig. 12-5). The equation of the curve is y = f(x) = h(1 – x²/b²) (a) in which b is the base and h is the height of the semisegment. Locate the centroid C of the semisegment. ...

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To determine the coordinates

\bar{x}[/latex...

Question: 11.8

A wood post of rectangular cross-section (Fig. 11-40) is constructed of structural grade, Douglas fir lumber (Fc = 15 MPa, E = 14 GPa). The cross-sectional dimensions are b = 120 mm and h = 160 mm. Assume that the supports provide pinned-end conditions, (a) Determine the allowable axial load Pallow ...

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We will use the AFPA formulas (Eqs. 11-88a. b. and...