Calculation Procedure:- Compute the properties of the section
The tables in the AISC Manual are helpful in calculating the moment of inertia. Thus Af
= 15 in^2 (96.8 cm^2 ); Aw = 24.75 in^2 (159.687 cm^2 ); / = 42,400 in^4 (176.481 dm^4 ); S =
1256 in^3 (20,585.8 cm^3 ).
For the T section comprising the flange and one-sixth the web, A = 15 + 4.13 = 19.13
in^2 (123.427 cm^2 ); then /= (1/12)(0.75)(20)^3 = 500 in^4 (2081.1 dm^4 ); r = (500/19.13)^05 =
5.11 in (129.794 mm); LYr = 18(12)75.11 =42.3. - Ascertain if the member satisfies the AISC Specification
Let h denote the clear distance between flanges, in (cm). Then: flange, ^(2O)A).75 = 13.3
< 16—this is acceptable; web, hltw = 66/0.375 = 176 < 320—this is acceptable. - Compute the allowable bending stress
Use /! = 22,000 - 0.679(1 Vr)^2 /Q, or fi = 22,000 - 0.679(42.3)^2 = 20,800 lb/in^2
(143,416.0 kPa); / 2 = 12,000,000/(L'^) = 12,000,000(15)/[18(12)(67.5)] = 12,300
lb/in^2 (84,808.5 kPa). Therefore, use 20,800 lb/in^2 (143,416.0 kPa) because it is the larger
of the two stresses. - Reduce the allowable bending stress In accordance with the
AISC Specification
Using the equation given in the Manual yields / 3 = 20,800(1 - 0.005(24.75/15)[176 -
24,000/(20,80O)
0
- 5
]} = 20,600 lb/in
2
(142,037.0 kPa).
- Determine the allowable bending moment
Use Af =/ 35 = 20.6(1256)712 = 2156 ft-kips (2923.5 kN-m).
ANALYSIS OFA RIVETED PLATE GIRDER
A plate girder is composed of one web plate 48 x^3 / 8 in (1219.2 x 9.53 mm); four flange
angles 6 x 4 x % in (152.4 x 101.6 x 19.05 mm); two cover plates 14 x y 2 in (355.6 x 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 7s-in (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:- Obtain the properties of the angles from the AISC Manual
Record the angle dimensions as shown in Fig. 7. - Check the cover plates for compliance with the
AISC Specification
The cover plates are found to comply with the pertinent sections of the Specification. - 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 in^2 (134.718 cm^2 ); area of rivet holes =
2C/2)(1)4(^3 /4)(1) = 4.00 in^2 (25.808 cm^2 ); allowable area of holes = 0.15(20.88) = 3.13.