Page 117 - Handbook of Civil Engineering Calculations, Second Edition

1.100 STRUCTURAL STEEL ENGINEERING AND DESIGN

At its ends, the girder will bear on masonry buttresses. The total depth of the girder is re-
stricted to approximately 70 in. (1778.0 mm). Select the cross section, establish the spac-
ing of the transverse stiffeners, and design both the intermediate stiffeners and the bearing
stiffeners at the supports.

Calculation Procedure:

1. Construct the shear and bending-moment diagrams
These diagrams are shown in Fig. 8.
2. Choose the web-plate dimensions
Since the total depth is limited to about 70 in. (1778.0 mm), use a 68-in. (1727.2-mm)
deep web plate. Determine the plate thickness, using the Specification limits, which are a
slenderness ratio h/t w of 320. However, if an allowable bending stress of 22,000 lb/sq.in.
(151,690.0 kPa) is to be maintained, the Specification imposes an upper limit of
7
(22,000) 0.5 162. Then t w h/162 68/162 0.42 in. (10.668 mm); use a /16-in.
2
(11.112-mm) plate. Hence, the area of the web A w 29.75 sq.in. (191.947 cm ).
3. Select the flange plates
2
Apply the approximation A f Mc/(2fy ) – A w /6, where y distance from the neutral axis
to the centroidal axis of the flange, in. (mm).
2
Assume 1-in. (25.4-mm) flange plates. Then A f 4053(12)(35)/[2(22)(34.5) ] –
2
29.75/6 27.54 sq.in. (177.688 cm ). Try 22 1 /4 in. (558.8 31.75 mm) plates with
1
2
A f 27.5 sq.in. (177.43 cm ). The width-thickness ratio of projection 11/1.25 8.8 <
16. This is acceptable.
Thus, the trial section will be one web plate 68 /16 in. (1727 11.11 mm); two
7
1
flange plates 22 1 /4 in. (558.8 31.75 mm).
4. Test the adequacy of the trial section
For this test, compute the maximum flexural and shearing stresses. Thus, I
(1/12)(0.438)(68) + 2(27.5)(34.63) 77,440 in (1,269,241.6 cm ); f Mc/I
3
2
3
3
4053(12)(35.25)/77,440 22.1 kips/sq.in. (152.38 MPa). This is acceptable. Also, v
207/29.75 6.96 < 14.5 kips/sq.in. (99.98 MPa). This is acceptable. Hence, the trial sec-
tion is satisfactory.
5. Determine the distance of the stiffeners from the girder ends
Refer to Fig. 8d for the spacing of the intermediate stiffeners. Establish the length of the
end panel AE. The Specification stipulates that the smaller dimension of the end panel
shall not exceed 11,000(0.438)/(6960) 0.5 57.8 < 68 in. (1727.2 mm). Therefore, provide
stiffeners at 56 in. (1422.4 mm) from the ends.
6. Ascertain whether additional intermediate stiffeners
are required
See whether stiffeners are required in the interval EB by applying the Specification
criteria.
Stiffeners are not required when h/t w < 260 and the shearing stress within the panel is
below the value given by either of two equations in the Specification, whichever equation
applies. Thus EB 396 – (56 + 96) 244 in. (6197.6 mm); h/t w 68/0.438 155 <
260; this is acceptable. Also, a/h 244/68 3.59.
In lieu of solving either of the equations given in the Specification, enter the table of
a/h, h/t w values given in the AISC Manual to obtain the allowable shear stress. Thus, with
a/h > 3 and h/t w 155, v allow 3.45 kips/sq.in. (23.787 MPa) from the table.