Mechanics of Materials 8th. Edition by James M. Gere, Barry J. Goodno | 9781111577742 | 1111577749

Mechanics of Materials

140 SOLVED PROBLEMS

8 SOLVED PROBLEMS

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.) ...

Verified Answer:

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

Question: 9.18

A simple beam with an overhang supports a uniform load of intensity q on span AB and a concentrated load P at end C of the overhang (Fig. 9-42). Determine the deflection δC and angle of rotation θC at point C. (Use the modified form of Castigliano’s theorem.) ...

Verified Answer:

Deflection

\delta_{C}

at the end of...

Question: 9.15

A simple beam AB of length L supports a uniform load of intensity q (Fig. 9-33). (a) Evaluate the strain energy of the beam from the bending moment in the beam. (b) Evaluate the strain energy of the beam from the equation of the deflection curve. (Note: The beam has constant flexural rigidity EI.) ...

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(a) Strain energy from the bending moment. The rea...

Question: 12.6

Determine the product of inertia Ixy of the Z-section shown in Fig. 12-23. The section has width b, height h, and constant thickness t. ...

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

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 ...

Verified Answer:

We will determine the moment of inertia

I_{...

Question: 12.2

The cross section of a steel beam is constructed of a HE 450A wide-flange section with 25 cm × 1.5 cm a cover plate welded to the top flange and a UPN 320 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: 12.4

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 and with respect to the centroidal axes xc and yc I . ...

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

Question: 12.1

A parabolic semisegment OAB is bounded by the x axis, the y axis, and a par-abolic 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} \text ...

Question: 12.3

Determine the moments of inertia Ix and Iy for the parabolic semiseg -ment OAB shown in Fig. 12-12. The equation of the parabolic boundary is y=f(x)=h(1-x^2/b^2)(a)(This same area was considered previously in Example 12-1.) ...

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To determine the moments of inertia by integration...

Question: 11.5

A steel wide-flange column of HE 320A shape (Fig. 11-29a) is pin supported at the ends and has a length of 7.5 m. The column supports a centrally applied load P1=1800 kN and an eccentrically applied loadP2=200 kN (Fig. 11-29b). 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: 9.12

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. ...

Verified Answer:

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: 10.5

A fixed-end beam AB supports a uniform load of intensity q acting over part of the span (Fig. 10-17a). Determine the reactions of this beam (that is, find the fixed-end moments and fixed-end forces). ...

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We can find the reactions of this beam by using su...

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. ...

Verified Answer:

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: 3.16

A circular tube and a square tube (Fig. 3-57) are constructed of the same material and subjected to the same torque. Both tubes have the same length, same wall thickness, and same cross-sectional area. What are the ratios of their shear stresses and angles of twist? (Disregard the effects of stress ...

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Use a four-step problem-solving approach. 1,2. Con...

Question: 3.12

A tapered bar AB of solid circular cross section is supported at the right-hand end and loaded by a torque T at the other end (Fig. 3-43). The diameter of the bar varies linearly from dA at the left-hand end to dB at the right-hand end. Determine the angle of rotation ΦA at end A of the bar by ...

Verified Answer:

Use a four-step problem-solving approach. Combine ...