Statics and Mechanics of Materials (5th Edition)
Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 11, Problem 1RP

Determine the shape factor for the wide-flange beam.

Chapter 11, Problem 1RP, Determine the shape factor for the wide-flange beam.

Expert Solution & Answer
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To determine

Find the shape factor for the wide-flange beam.

Answer to Problem 1RP

The shape factor for the wide-flange beam is k=1.22_.

Explanation of Solution

Show the free-body diagram of the beam as in Figure 1.

Statics and Mechanics of Materials (5th Edition), Chapter 11, Problem 1RP , additional homework tip  1

Consider the beam as rectangular and determine the moment of inertia for rectangular section and deduct the moment of inertia of the two smaller rectangular portions.

Determine the moment of inertia of the I-section using the formula.

I=BD3122×bd312

Here, B is width of rectangular section, D is depth of large rectangular section, b is depth of small rectangular section, and d is depth of small rectangular section.

Substitute 180 mm for B, 220 mm for D, 75 mm for b, and 180 mm for d.

I=180×2203122×75×180312=86,820,000mm4×1m4(1,000mm)4=86.82×106m4

Determine the elastic moment using the equation.

MY=σYIc

Here, σY is allowable stress in the beam and c is the distance between the neutral axis and the extreme fibre in the beam.

Substitute 86.82×106m4 for I and 110 mm for c.

MY=σY×86.82×106110mm×1m1,000mm=(0.78927×103)σY

Show the free-body diagram of the profile view of the I-beam as in Figure 2.

Statics and Mechanics of Materials (5th Edition), Chapter 11, Problem 1RP , additional homework tip  2

Determine the plastic moment in the I-section using the equation.

Mp=σYA1c1+σYA2c2=σYb1h1c1+σYb2h2c2

Here, A1 is area of flanges, c1 is the distance between the centre to centre of flanges where the force is resultant, A2 is the area of web, and c2 is the distance between the centre to centre of web where the force is resultant.

Substitute 180 mm for b1, 20 mm for h1, 200 mm for c1, 30 mm for b2, 90 mm for h2, and 90 mm for c2.

Mp=(σY×180mm×1m1,000mm×20mm×1m1,000mm×200mm×1m1,000mm+σY×30mm×1m1,000mm×90mm×1m1,000mm×90mm×1m1,000mm)=(0.963×103)σY

Determine the shape factor for the I-section using the formula.

k=MpMY

Substitute (0.963×103)σY for Mp and (0.78927×103)σY for MY.

k=(0.963×103)σY(0.78927×103)σY=1.22

Thus, the shape factor for the wide-flange beam is k=1.22_.

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Chapter 11 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 11.2 - Draw the shear and moment diagrams for the beam,...Ch. 11.2 - Draw the shear and moment diagrams for the beam,...Ch. 11.2 - Express the shear and moment in terms of x for 0 ...Ch. 11.2 - Express the internal shear and moment in the...Ch. 11.2 - Prob. 6PCh. 11.2 - Express the internal shear and moment in terms of...Ch. 11.2 - Draw the shear and moment diagrams for the beam,...Ch. 11.2 - If the force applied to the handle of the load...Ch. 11.2 - Draw the shear and moment diagrams for the shaft....Ch. 11.2 - The crane is used to support the engine, which has...Ch. 11.2 - Prob. 12PCh. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Members ABC and BD of the counter chair are...Ch. 11.2 - A reinforced concrete pier is used to support the...Ch. 11.2 - Draw the shear and moment diagrams for the beam...Ch. 11.2 - The industrial robot is held in the stationary...Ch. 11.2 - Determine the placement distance a of the roller...Ch. 11.2 - Prob. 20PCh. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Draw the shear and moment diagrams for the...Ch. 11.2 - The 150-lb man sits in the center of the boat,...Ch. 11.2 - Prob. 24PCh. 11.2 - The footing supports the load transmitted by the...Ch. 11.2 - Prob. 26PCh. 11.2 - Prob. 27PCh. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Prob. 30PCh. 11.2 - Prob. 31PCh. 11.2 - Prob. 32PCh. 11.2 - The shaft is supported by a smooth thrust bearing...Ch. 11.2 - Draw the shear and moment diagrams for the...Ch. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Draw the shear and moment diagrams for the rod....Ch. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - Prob. 38PCh. 11.2 - Draw the shear and moment diagrams for the double...Ch. 11.2 - Draw the shear and moment diagrams for the simply...Ch. 11.2 - The compound beam is fixed at A, pin connected at...Ch. 11.2 - Draw the shear and moment diagrams for the...Ch. 11.2 - The compound beam is fixed at A, pin connected at...Ch. 11.2 - Draw the shear and moment diagrams for the beam....Ch. 11.2 - A short link at B is used to connect beams AB and...Ch. 11.2 - The truck is to be used to transport the concrete...Ch. 11.4 - Determine the moment of inertia of the cross...Ch. 11.4 - Prob. 3PPCh. 11.4 - In each case, show how the bending stress acts on...Ch. 11.4 - Prob. 5PPCh. 11.4 - If the beam is subjected to a bending moment of M...Ch. 11.4 - If the beam is subjected to a bending moment of M...Ch. 11.4 - If the beam is subjected to a bending moment of M...Ch. 11.4 - Prob. 12FPCh. 11.4 - If the beam is subjected to a bending moment of M...Ch. 11.4 - An A-36 steel strip has an allowable bending...Ch. 11.4 - Determine the moment M that will produce a maximum...Ch. 11.4 - Determine the maximum tensile and compressive...Ch. 11.4 - The beam is constructed from four pieces of wood,...Ch. 11.4 - The beam is constructed from four pieces of wood,...Ch. 11.4 - The beam is made from three boards nailed together...Ch. 11.4 - Prob. 53PCh. 11.4 - If the built-up beam is subjected to an internal...Ch. 11.4 - If the built-up beam is subjected to an internal...Ch. 11.4 - Prob. 56PCh. 11.4 - Determine the moment M that should be applied to...Ch. 11.4 - Prob. 58PCh. 11.4 - Prob. 59PCh. 11.4 - The beam is subjected to a moment of 15 kip ft....Ch. 11.4 - The beam is subjected to a moment of 15 kip ft....Ch. 11.4 - Prob. 62PCh. 11.4 - The steel shaft has a diameter of 2 in. It is...Ch. 11.4 - The beam is made of steel that has an allowable...Ch. 11.4 - Prob. 65PCh. 11.4 - Solve Prob. 11-65 if the moment M = 50 N m is...Ch. 11.4 - The shaft is supported by smooth journal bearings...Ch. 11.4 - Prob. 68PCh. 11.4 - Prob. 69PCh. 11.4 - The strut on the utility pole supports the cable...Ch. 11.4 - Prob. 71PCh. 11.4 - Prob. 72PCh. 11.4 - Determine the smallest allowable diameter of the...Ch. 11.4 - Prob. 74PCh. 11.4 - The shaft is supported by a thrust bearing at A...Ch. 11.4 - If the intensity of the load w = 15 kN/m,...Ch. 11.4 - If the allowable bending stress is allow = 150...Ch. 11.4 - The beam is subjected to the triangular...Ch. 11.4 - The beam has a rectangular cross section with b =...Ch. 11.4 - Determine the absolute maximum bending stress in...Ch. 11.4 - If the compound beam in Prob. 11-42 has a square...Ch. 11.4 - Prob. 82PCh. 11.4 - Prob. 83PCh. 11.4 - Determine, to the nearest millimeter, the smallest...Ch. 11.4 - Prob. 85PCh. 11.4 - Determine the absolute maximum bending stress in...Ch. 11.4 - Determine the smallest diameter of the shaft to...Ch. 11.4 - Prob. 88PCh. 11.4 - A log that is 2 ft in diameter is to be cut into a...Ch. 11.4 - The simply supported truss is subjected to the...Ch. 11.4 - Prob. 92PCh. 11.4 - Prob. 93PCh. 11.4 - Prob. 94PCh. 11.4 - The beam has the rectangular cross section shown....Ch. 11.5 - Determine the bending stress developed at corners...Ch. 11.5 - Prob. 15FPCh. 11.5 - Prob. 96PCh. 11.5 - Prob. 97PCh. 11.5 - Prob. 98PCh. 11.5 - Prob. 99PCh. 11.5 - Determine the bending stress at point A of the...Ch. 11.5 - The steel shaft is subjected to the two loads. If...Ch. 11.5 - Prob. 102PCh. 11.5 - Prob. 103PCh. 11.5 - Prob. 104PCh. 11 - Determine the shape factor for the wide-flange...Ch. 11 - The compound beam consists of two segments that...Ch. 11 - A shaft is made of a polymer having a parabolic...Ch. 11 - Determine the maximum bending stress in the handle...Ch. 11 - Determine the shear and moment in the beam as...Ch. 11 - A wooden beam has a square cross section as shown....Ch. 11 - Prob. 7RPCh. 11 - The strut has a square cross section a by a and is...
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