Thin pieces of wrought-iron under compression endwise may neither crush nor deflect (bend), but give way by wrinkling, that is, buckling or corrugating, provided there are no stiffening-ribs lengthwise.

Thus a square, tubular column, if the sides are very thin might give way, as shown in Figure 2, which is called wrinkling. Or, in a similar way, the top plate of a boxed girder, if very thin, might wrinkle, as shown in Figure 3, under heavy compressive strains. To calculate this strain use the following formula: b = d. (wr/w)2 (4)

Where w - the amount of ultimate compression in pounds per square inch, which will wrinkle the material.

wr = a constant, d = the thickness of plate in inches,

Wrinkling Strains 10056

Fig. 2.

b = the unstiffened breadth of plate in inches. IE a plate has stiffening ribs along both edges, use for b the actual breadth between the stiffening ribs; if the plate is stiffened along one edge only, use 4bl in place of b. Thus, in the case of the boxed girder, Figure 3, if we were considering the part of top plate between the webs, we should use for b in the formula, the actual breadth of b in inches; while, if we were considering the overhanging part b1 of top plate, we should use 4b1 in place of b in formula. For rectangular columns use 160,000 pounds for wr; for tubular beams, top plates of girders, and single plates use 200,000 pounds for wr. With a factor-of-safety of 3, we should have 16000/3 = 53000 pounds for rectangular columns, and 200000/3 = 66000 pounds for tubular beams, top plates of riveted girders and single plates.

Wrinkling Strains 10057

Fig. 3.

For to we shall use, of course, 36000/3 12000 pounds, which is the safe allowable compressive strain. This would give the following table for safe unstiffened breadth of wrought-iron plates, to prevent wrinkling of plates.

Table III

Safe breadth in inches of Plate stiffened along both edges.

(use b.)

Safe breadth in inches of Plate stiffened along one edge only.

(use 4b1)

Thickness of

Plate in inches.

Rectangular Columns.

Tubular Beams, riveted Girders, and single Plates.

Rectangular Columns.

Riveted Girders and single Plates.

Table III 10058

Table III 10059

Table III 10060

Table III 10061

1/8

2 7/16

3 3/4

5/8

15/16

1/4

4 7/8

7 9/16

1 1/4

1 7/8

3/8

7 5/16

11 3/8

1 7/8

2 13/18

1/2

9 3/4

15 1/8

2 7/16

3 3/4

5/8

12 3/16

18 7/8

3

4 11/16

3/4

14 5/8

22 11/16

3 11/16

5 5/8

7/8

17 1/16

26 1/2

4 1/4

6 9/16

1

19 1/2

30 1/4

4 7/8

7 9/16

1 1/4

24 3/8

37 13/16

6 1/8

9 7/16

1 1/2

29 1/4

45 3/8

7 5/16

11 5/16

1 3/4

34 1/8

52 15/16

8 9/16

13 3/16

2

39

60 1/2

9 3/4

15 1/8

The above table will cover every case likely to arise in buildings.

Two facts should be noticed in connection with wrinkling:

1. That the length of plate does not in any way affect the resistance to wrinkling, which is dependent only on the breadth and thickness of the part of plate unstiffened, and

2. That the resistance of plates to wrinkling being dependent on their breadth and thickness only, to obtain equal resistance to wrinkling at all points (in rectangular columns with uneven sides), the thickness of each side should be in proportior to its breadth.

Thus, if we have a rectangular column 30" X 15" in cross section and the 30" side is 1" thick, we should make the 15" side but 1/2" thick, for as 30": 1": : 15": 1/2".

Of course, we must also calculate the column for direct crushing and flexure, and in the case of beams for rupture and deflection, as well as for wrinkling.

It is desired to make the top plate of a boxed girder as wide as possible, the lop flange is to be l 1/4" thick, and is to be subjected to the full amount of the safe compressive strain, viz: 12,000 pounds per square inch; how wide apart should the webs be placed, and how much can the plate overhang the angles without danger of wrinkling? Each web to be 1/2" thick, and the angles 4" X 4" each?

For the distance between webs we use b in Formula (4). b = 1 1/4 (66000/12000)2 = 1 1/4. 5 1/22 = 37 13/16" which is the safe width between webs to avoid wrinkling

For the overhanging part of top plate we must use 4b1 in place of b in Formula (4).

4b1 = 1 1/4 (66000/12000)2 = 37 13/16, therefore, b1 =( 37 13/16)/4 = 9,453, or say, b1 = 9 7/16".

The total width of top plate will be, therefore, including 1" for two webs and 8" for the two angles, or 9", and remembering that there is an overhanging part, b1, each side,

9" + b + b1 + b1

= 9 + 37 13/16 + 9 7/16 + 9 7/16

= 65 11/16".

By referring to Table III, we should have obtained the same result, without the necessity of any calculation. Figure 4 will make the above still more clear.

Table III 10062

Fig. 4