Page 118 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.101

At E, V 207 – 4.67(4) 188 kips (836.2 kN); v 188/29.75 6.32 kips/sq.in.
(43.576 MPa) > 3.45 kips/sq.in. (23.787 MPa); therefore, intermediate stiffeners are
required in EB.
7. Provide stiffeners, and investigate the suitability of their
tentative spacing
Provide stiffeners at F, the center of EB. See whether this spacing satisfies the Specifica-
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tion. Thus [260/(h/t w )] (260/155) 2.81; a/h 122/68 1.79 < 2.81. This is
acceptable.
Entering the table referred to in step 6 with a/h 1.79 and h/t w 155 shows v allow
7.85 > 6.32. This is acceptable.
Before we conclude that the stiffener spacing is satisfactory, it is necessary to investi-
gate the combined shearing and bending stress and the bearing stress in interval EB.
8. Analyze the combination of shearing and bending stress
This analysis should be made throughout EB in the light of the Specification require-
ments. The net effect is to reduce the allowable bending moment whenever V >
0.6V allow . Thus, V allow 7.85(29.75) 234 kips (1040.8 kN); and 0.6(234) 140 kips
(622.7 kN).
In Fig. 8b, locate the boundary section G where V 140 kips (622.7 kN). The allow-
able moment must be reduced to the left of G. Thus, AG (207 – 140)/4 16.75 ft
(5.105 m); M G 2906 ft·kips (3940.5 kN·m); M E 922 ft·kips (1250.2 kN·m). At G,
M allow 4053 ft·kips (5495.8 kN·m). At E, f allow [0.825 – 0.375(188/234)](36) 18.9
kips/sq.in. (130.31 MPa); M allow 18.9(77,440)/[35.25(12)] 3460 ft·kips (4691.8 kN·m).
In Fig. 8c, plot points E
and G
to represent the allowable moments and connect these
points with a straight line. In all instances, M < M allow .
9. Use an alternative procedure, if desired
As an alternative procedure in step 8, establish the interval within which M > 0.75M allow
and reduce the allowable shear in accordance with the equation given in the Specification.
10. Compare the bearing stress under the uniform load
with the allowable stress
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The allowable stress given in the Specification f b,allow [5.5 + 4/(a/h) ]10,000/(h/t w ) 2
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kips/sq.in. (MPa), or, for this girder, f b,allow (5.5 + 4/1.79 )10,000/155 2.81
kips/sq.in. (19.374 MPa). Then f b 4/[12(0.438)] 0.76 kips/sq.in. (5.240 MPa). This is
acceptable. The stiffener spacing in interval EB is therefore satisfactory in all respects.
11. Investigate the need for transverse stiffeners
in the center interval
Considering the interval BC, V 32 kips (142.3 kN); v 1.08 kips/sq.in. (7.447 MPa);
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a/h 192/68 2.82 [260/(h/t w )] .
The Manual table used in step 6 shows that v allow > 1.08 kips/sq.in. (7.447 MPa); f b,al-
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low (5.5 + 4/2.82 )10,000/155 2.49 kips/sq.in. (17.169 MPa) > 0.76 kips/sq.in.
(5.240 MPa). This is acceptable. Since all requirements are satisfied, stiffeners are not
needed in interval BC.
12. Design the intermediate stiffeners in accordance
with the Specification
For the interval EB, the preceding calculations yield these values: v 6.32 kips/sq.in.
(43.576 MPa); v allow 7.85 kips/sq.in. (54.125 MPa). Enter the table mentioned in step 6
with a/h 1.79 and h/t w 155 to obtain the percentage of web area, shown in italics in
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the table. Thus, A st required 0.0745(29.75)(6.32/7.85) 1.78 sq.in. (11.485 cm ). Try
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two 4 /4 in. (101.6 6.35 mm) plates; A st 2.0 sq.in. (12.90 cm ); width-thickness ra-
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4
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tio 4/0.25 16. This is acceptable. Also, (h/50) (68/50) 3.42 in (142.351 cm );