Page 114 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.97

Calculation Procedure:

1. Compute the properties of the section
The tables in the AISC Manual are helpful in calculating the moment of inertia. Thus
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A f 15 sq.in. (96.8 cm ); A w 24.75 sq.in. (159.687 cm ); I 42,400 in (176.481
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dm ); S 1256 in (20,585.8 cm ).
For the T section comprising the flange and one-sixth the web, A 15 + 4.13 19.13
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sq.in. (123.427 cm ); then I (1/12)(0.75)(20) 500 in (2081.1 dm ); r (500/19.13) 0.5
5.11 in. (129.794 mm); L
/r 18(12)/5.11 42.3.
2. Ascertain if the member satisfies the AISC Specification
Let h denote the clear distance between flanges, in. (cm). Then: flange, /2(20)/0.75
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13.3 < 16—this is acceptable; web, h/t w 66/0.375 176 < 320—this is acceptable.
3. Compute the allowable bending stress
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Use f 1 22,000 – 0.679(L
/r) /C b , or f 1 22,000 – 0.679(42.3) 20,800 lb/sq.in.
(143,416.0 kPa); f 2 12,000,000/(L
d/A f ) 12,000,000(15)/[18(12)(67.5)] 12,300
lb/sq.in. (84,808.5 kPa). Therefore, use 20,800 lb/sq.in. (143,416.0 kPa) because it is the
larger of the two stresses.
4. Reduce the allowable bending stress In accordance with the
AISC Specification
Using the equation given in the Manual yields f 3 20,800{1 – 0.005(24.75/15)[176 –
0.5
24,000/(20,800) ]} 20,600 lb/sq.in. (142,037.0 kPa).
5. Determine the allowable bending moment
Use M f 3 S 20.6(1256)/12 2156 ft·kips (2923.5 kN·m).
ANALYSIS OF A RIVETED PLATE GIRDER
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A plate girder is composed of one web plate 48 /8 in. (1219.2 9.53 mm); four
flange angles 6 4 /4 in. (152.4 101.6 19.05 mm); two cover plates 14 /2 in.
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(355.6 12.7 mm). The flange angles are set 48.5 in. (1231.90 mm) back to back with
their 6-in. (152.4-mm) legs outstanding; they are connected to the web plate by /8-in.
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(22.2-mm) rivets. If the member has continuous lateral support, what bending moment
may be applied? What spacing of flange-to-web rivets is required in a panel where the
vertical shear is 180 kips (800.6 kN)?
Calculation Procedure:

1. Obtain the properties of the angles from the AISC Manual
Record the angle dimensions as shown in Fig. 7.
2. Check the cover plates for compliance with the
AISC Specification
The cover plates are found to comply with the pertinent sections of the Specification.
3. Compute the gross flange area and rivet-hole area
Ascertain whether the Specification requires a reduction in the flange area. Therefore
gross flange area 2(6.94) + 7.0 20.88 sq.in. (134.718 cm ); area of rivet holes
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2( /2)(1)4( /4)(1) 4.00 sq.in. (25.808 cm ); allowable area of holes 0.15(20.88) 3.13.
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