Page 191 - Handbook of Civil Engineering Calculations, Second Edition

1.174 STRUCTURAL STEEL ENGINEERING AND DESIGN

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with respect to line 3. Then a /2(24 – 18.25) 2.88 in. (73.2 mm); M 3 633.3 in.·kips
(71.6 kN·m).
With reference to Fig. 6b, the tensile force F y in the rivet is usually limited by the
bending capacity of beam flange. As shown in the AISC Manual, the standard gage in the
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W18 60 is 3 /2 in. (88.9 mm). Assume that the point of contraflexure in the beam
flange lies midway between the center of the rivet and the face of the web. Referring to
Fig. 4b, we have c /2(1.75 – 0.416/2) 0.771 in. (19.6 mm); M allow fS
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27( /6)(3)(0.695) 0.52 in.·kips (0.74 kN·m). If the compressive force C is disregarded,
F y,allow 6.52/0.771 8.46 kips (37.6 kN)
Try 16 rivets. The moment on the rivet group is M 633.3 – 13.35(14.5) 440 in.·kips
(49.7 kN·m). By Eq. 3, S 2(3)(8)(9)/6 72 in. (1829 mm). Also, F y 440/72 +
13.35/16 6.94 < 8.46 kips (37.6 kN). This is acceptable. (The value of F y correspon-
ding to 14 rivets is excessive.)
The rivet stresses are s t 6.94/0.6013 11.54 kips/sq.in. (79.6 MPa); s s 64.11/
[16(0.6013)] 6.67 kips/sq.in. (45.9 MPa). From the Specification, s t,allow 28 –
1.6(6.67) 17.33 kips/sq.in. (119.5 MPa). This is acceptable. The use of 16 rivets is
therefore satisfactory.
8. Compute the stresses in the bracket at the toe of the fillet
(line 4)
Since these stresses are seldom critical, take the length of the bracket as 24 in. (609.6
mm) and disregard the eccentricity of V. Then M 633.3 – 64.11(1.18) 558 in.·kips
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2
(63.1 kN·m); f 558/[( /6)(0.416)(24) ] + 13.35/[0.416(24)] 15.31 kips/sq.in. (105.5
MPa). This is acceptable. Also, v 1.5(64.11)/[0.416(24)] 9.63 kips/sq.in. (66.4 MPa)
This is also acceptable.

DESIGN OF A WELDED FLEXIBLE
BEAM CONNECTION

A W18 64 beam is to be connected to the flange of its supporting column by means
of a welded framed connection, using E60 electrodes. Design a connection to transmit
a reaction of 40 kips (177.9 kN). The AISC table of welded connections may be ap-
plied in selecting the connection, but the design must be verified by computing the
stresses.

Calculation Procedure:

1. Record the pertinent properties of the beam
It is necessary to investigate both the stresses in the weld and the shearing stress in the
beam induced by the connection. The framing angles must fit between the fillets of the
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beam. Record the properties: T 15 /8 in. (390.5 mm); t w 0.403 in. (10.2 mm).
2. Select the most economical connection from the AISC Manual
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The most economical connection is: angles 3 3 /16 in. (76 76 7.9 mm), 12 in.
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(305 mm) long; weld size > /16 in. (4.8 mm) for connection to beam web, /4 in. (6.4 mm)
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for connection to the supporting member.
According to the AISC table, weld A has a capacity of 40.3 kips (179.3 kN), and weld
B has a capacity of 42.8 kips (190.4 kN). The minimum web thickness required is 0.25 in.
(6.4 mm). The connection is shown in Fig. 7a.