Mechanics of Materials, 7th Edition
Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Chapter 1, Problem 66RP

In the steel structure shown, a 6-mm-diameter pin is used at C and 10-mm-diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired, determine the largest load P that can be applied at A. Note that link BD is not reinforced around the pin holes.

Fig. P1.66

Chapter 1, Problem 66RP, In the steel structure shown, a 6-mm-diameter pin is used at C and 10-mm-diameter pins are used at B

Expert Solution & Answer
Check Mark
To determine

The largest load P that can be applied at A.

Answer to Problem 66RP

The largest load P that can be applied at A is 1.683kN_.

Explanation of Solution

Given information:

The diameter of the pin at C is 6mm.

The diameter of the pin at B and D is 10mm.

The ultimate normal stress (τU) is 150MPa.

The ultimate normal stress (σU) is 400MPa

The factor of safety is 3.0.

Calculation:

Sketch the free body diagram of ABC as shown in Figure 1.

Mechanics of Materials, 7th Edition, Chapter 1, Problem 66RP

Refer to Figure 1.

Taking moment about C.

Mc=0

0.280P0.120FBD=00.280P=0.120FBDP=0.42857FBD (1)

Taking moment about B

MB=0

0.160P0.120C=00.160P=0.120CP=0.75C (2)

Find the area of tension on net section of link BD using the relation:

Anet=dc(tdBD) (3)

Here, t is the thickness of the section, dc is the diameter of pin C, and dBD is diameter of pin at B and D.

Substitute 6mm for dc, 18mm for t, and 10mm for dBD in Equation (3).

Anet=6(1810)=48mm2(1m106mm)2=4.8×105m2

Find the force in member BD on net section of link BD using the relation:

FBD=σAnet (4)

Here, Anet is the area of tension on net section of link BD.

Modify Equation (4).

FBD=σUF.S.Anet (5)

Substitute 400MPa for σU, 3 for F.S., and 4.8×105m2 for Anet in Equation (5).

FBD=400MPa(106Pa1MPa)3×(4.8×105)=400×1063×(4.8×105)=6,400N

Find the area of shear in pins BD using the relation:

Apin=πd24 (6)

Substitute 10mm for d in Equation (6).

Apin=π(10)24=78.54mm2(1m2106mm2)=7.854×105m2

Find the force in member BD shear in pins BD using the relation:

FBD=τApin (7)

Here, Apin is the shear in pins at BD.

Modify Equation (7).

FBD=τUF.S.Apin (8)

Substitute 150MPa for τU, 3 for F.S., and 7.854×105m2 for Anet in Equation (8).

FBD=15400MPa(106Pa1MPa)3×(4.8×105)=150×1063×(7.8539×105)=3,926N

Select the smaller value of FBD is 3,926N.

Find the value of P as follows:

Substitute 3,926N for P in Equation (1).

P=0.428×3,926=1,682.5=1,683N(1kN103N)=1.683kN

Find the shear in pin at C using the relation:

Apin=πd24 (9)

Substitute 6mm for d in Equation (9).

Apin=π(6)24=28.27mm2(1m2106mm2)=2.8274×105m2

Find the value of C shear in pins C using the relation:

C=2τApin (10)

Here, Apin is the shear in pins at C.

Modify Equation (10).

C=2(τUF.S.)Apin (11)

Substitute 150MPa for τU, 3 for F.S., and 2.8274×105m2 for Anet in Equation (11).

C=2(150MPa(106Pa1MPa)3)×(2.8274×105)=2(150×1063)×(7.8539×105)=2,827N

Find the largest load P such that be applied at A.

Substitute 2,827N for C in Equation (2).

P=0.75×2,827=2,120N

Select the smaller value of P.

Thus, the largest load P such that be applied at A is 1.683kN_.

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Chapter 1 Solutions

Mechanics of Materials, 7th Edition

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