Mechanics of Materials by James M. Gere, Barry J. Goodno | 9781111136031 | 1111136033 | Holooly

Mechanics of Materials

Mechanics of Materials

77 SOLVED PROBLEMS

Question: 5.7

A simple beam AB of span length 21 ft must support a uniform load q = 60 kN/m 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 110 MPa, select a structural steel beam of ...

Verified Answer:

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

Question: 9.1

A long, slender column ABC is pin-supported at the ends and compressed by an axial load P (Fig. 9-14). 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: 8.9

A simple beam AB of span length L has an overhang BC of length a (Fig. 8-21a). 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. 8-21c). (Note: The beam has constant flexural rigidity EI.) ...

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

Question: 8.8

A compound beam ABC has a roller support at A, an internal hinge at B, and a fixed support at C (Fig. 8-20a). Segment AB has length a and segment BC has length b. A concentrated load P acts at distance 2a/3 from support A and a uniform load of intensity q acts between points B and C. Determine ...

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For purposes of analysis, we will consider the com...

Question: 8.7

A cantilever beam AB with a uniform load of intensity q acting on the right-hand half of the beam is shown in Fig. 8-19a. Obtain formulas for the deflection δB and angle of rotation θB at the free end (Fig. 8-19c). (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: 5.5

A simply supported wood beam having a span length L = 3 m carries a uniform load q = 4 kN/m (Fig. 5-19). The allowable bending stress is 12 MPa, the wood weighs 5.4 kN/m³, 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: 7.3

The rotor shaft of a helicopter drives the rotor blades that provide the lifting force to support the helicopter in the air (Fig. 7-17a). As a consequence, the shaft is subjected to a combination of torsion and axial loading (Fig. 7-17b). For a 50-mm diameter shaft transmitting a torque T = 2.4 ...

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The stresses in the rotor shaft are produced by th...

Question: 9.2

A viewing platform in a wild-animal park (Fig. 9-20a) is supported by a row of aluminum pipe columns having length L=3.25 m and outer diameter d=100 mm. The bases of the columns are set in concrete footings and the tops of the columns are supported laterally by the platform. The columns are being ...

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Critical load. Because of the manner in which the ...

Question: 8.5

A simple beam AB with an overhang BC supports a concentrated load P at the end of the overhang (Fig. 8-15a). 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. 8-15b). ...

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Differential equations of the deflection curve. Be...

Question: 8.4

Determine the equation of the deflection curve for a cantilever beam AB supporting a triangularly distributed load of maximum intensity q0 (Fig. 8-14a). Also, determine the deflection δB and angle of rotation θB at the free end (Fig. 8-14b). Use the fourth-order differential equation of the ...

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Differential equation of the deflection curve. The...

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