Mechanics of Materials CIVL 3322 / MECH 3322

Shear Flow and Beam Construction

Shear Flow and Beam Construction 2

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9.40 A wooden beam is fabricated from one 2 × 10 and two 2 × 4 pieces of dimension lumber to form the I-beam cross section shown in Fig. P9.40. The flanges of the beam are fastened to the web with nails that can safely transmit a force of 120 lb in direct shear. If the beam is simply supported and carries a 1,000-lb load at the center of a 12-ft span, determine: (a) the horizontal force transferred from each flange to the web in a 12-in. long segment of the beam. (b) the maximum spacing s (along the length of the beam) required for the nails. (c) the maximum horizontal shear stress in the I-beam.

Fig. P9.40

Solution Moment of inertia about the z axis:

Shape Width b Height h IC d = yi – y d²A IC + d²A (in.) (in.) (in.4) (in.) (in.4) (in.4)

top flange 4 2 2.667 6.000 288.000 290.667 web 2 10 166.667 0.000 0.000 166.667 bottom flange 4 2 2.667 –6.000 288.000 290.667

Moment of inertia about the z axis (in.4) = 748.000

Maximum shear force For P = 1,000 lb, V = P/2 = 500 lb (a) Horizontal force transferred from each flange (in a 12-in. length):

3

3

4

(4 in.)(2 in.)(6 in.) 48 in.

(500 lb)(48 in. )32.086 lb/in.

748 in.(32.086 lb/in.)(12 38 5 li bn.)H

QVQ

qI

F Ans. (b) Maximum nail spacing:

(1 nail)(120 lb/nail)

32.086 3.74 in

lb/ n.

i .

f f

f f

q s n V

n Vs

q Ans.

(c) Maximum horizontal shear stress:

3max

3

max 4

(4 in.)(2 in.)(6 in.) (2 in.)(5 in.)(2.5 in.) 73 in.

(500 lb)(73 in. )(748 in. )(2 in.)

24.4 psi

Q

Ans.

Homework

¢ Problem P9.41 ¢ Problem P9.43 ¢ Problem P9.45

Shear Flow and Beam Construction 3