This section is from the "Architectural Iron And Steel, And Its Application In The Construction Of Buildings" book, by WM. H. Birkmire.. Also see Amazon: Architectural Iron And Steel, And Its Application In The Construction Of Buildings.

The foregoing remarks apply also to channels, which are seldom used singly as struts, but frequently in pairs. When so used, if the methods of connection are not of such a nature as to insure the unity of action of the pair, they should be treated as an assemblage of separate struts.

But if connected by a proper system of triangular latticing, the pair can be considered as a unit, and each channel treated as a series of short struts whose length is the distance between centres of latticing.

As described by diagram of angle in table for even legs, the angle is considered free to yield in its weakest direction, that is, in the direction of the least radius of gyration.

If the angle is prevented from failing in this direction by bracing or otherwise, its resistance will be increased to some extent, and a correction can be made by taking the greatest instead of the least radius of gyration into calculation.

An angle strut with flat ends, whose dimensions are 4 X 4 X 3/8 inches and 12 feet long, has a least radius of gyration of .81 inch and greatest radius of gyration 1.24.

When the strut has no lateral support the value of l/r will be 144/.88 = 178. By table, the nearest equals 3500 pounds per square inch.

If this strut is now braced so that it cannot fail in the weakest direction, that is, in the line of a diagonal from the corner of the angle, but is free to fail in the direction of its legs, then the value of l/r becomes 144/1.24 = 116, and the safe load, by the table, becomes 6260 pounds per square inch.

For single uneven tees, find the least radius of gyration from table of Tees, and proceed as described for angle struts. This also applies to even-legged tees.

When a pair of uneven tees are braced together in the direction of the shorter leg, they form a single strut, whose least radius of gyration is the same as the greatest radius of gyration for a single tee.

Therefore when determining the resistance of the combined strut, take the greatest radius of gyration from the table of uneven-leg tees, and the least radius of gyration when determining the distance between centres of lateral bracing.

A.pair of uneven tees 5 X 2 1/2 inches, whose total area is 6.14 square inches, are braced together in the direction of the shorter leg, forming a single hinged-ended strut 15 feet long.

What is the greatest safe load, and what the greatest distance between centres of lateral bracing?

By the .table of tees, the greatest radius of gyration = 1.14 inches; l/r = 158, which gives, by table, 3060 pounds per square inch, or 18,788 pounds as the total greatest safe load.

Least radius of gyration = .72, which multiplied by 158 gives 113 inches as the greatest distance between centres of lateral bracing.

Experiments thus far made upon steel struts indicate that for lengths up to 90 radii of gyration their ultimate strength is about 20% higher than for iron. Beyond this point the excess of strength diminishes until it becomes zero at about 200 radii. After passing this limit the compressive resistance of steel and iron seems to become practically equal.

Size in inches. | Weight per yard. | Areas in square inches. | Radii of Gyration. | |||

Web. | Total. | Axis AB. | Axis CD, | |||

15 | 200 | 11.86 | 8.04 | 19.90 | 5.86 | 1.20 |

15 | 145 | 8.97 | 5.58 | 14.55 | 5.98 | I.08 |

12 | 168 | 10.66 | 6.23 | 16.89 | 4.69 | 1.17 |

12 | I20 | 7.42 | 4.53 | 11.95 | 4.78 | 1.01 |

10 1/2 | 134 | 9.57 | 3.87 | 13.44 | 4.24 | 1.19 |

10 1/2 | 108 | 7.33 | 3.50 | 10.83 | 4.25 | 1.07 |

10 1/2 | 89 | 5.91 | 3.3 | 8.94 | 4.26 | •97 |

10 | 112 | 7.23 | 3.94 | 11.17 | 3.94 | .98 |

IO | 90 | 6.29 | 2.75 | 9.04 | 4.05 | •95 |

9 | 90 | 6.15 | 2.92 | 9.07 | 3.62 | .96 |

9 | 70 | 4.77 | 2.21 | 6.98 | 3.68 | .89 |

8 | 8l | 5.53 | 2.56 | 8.14 | 3.21 | .94 |

8 | 65 | 4.50 | 2.03 | 6.53 | 3.25 | .83 |

7 | 65 | 4.17 | 2.41 | 6.58 | 2.75 | •79 |

7 | 52 | 3.84 | 1.30 | 5.14 | 2.89 | .82 |

6 | 50 | 3.16 | 1.88 | 5.04 | 2.31 | .65 |

6 | 40 | 2.91 | 1.17 | 4.08 | 2.43 | .66 |

5 | 34 | 2.13 | 1.25 | 3.38 | 1.99 | .60 |

5 | 30 | 2.06 | .88 | 2.94 | 2.06 | .60 |

4 | 28 | 2.15 | .75 | 2.90 | 1.63 | .63 |

4 | 18.5 | 1.34 | .56 | 1.90 | 1.65 | .51 |

3 | 23 | 1.72 | •53 | 2.25 | 1.21 | •59 |

Articles 98 and 99 give the radii of gyration for many of the sections in ordinary use. For any other section desired, refer to "Properties of Beams and Channels," in Chapter II (Floors), which gives the moment of inertia of a greater variety of sections. The greatest radius of gyration can be found by the following formula:

R=รป(I/A) width of flange/4.58; The least radius of gyration of I beams =

" " " " " " channels = width of flange/3.54.

Size in inches. | Weight per yard. | Areas in square inches. | Radii of Gyration. | Distance. d, from Base to Neutral Axis. | |||

Flanges. | Web. | Total. | Axis A B. | Axis CD. | |||

15 | 148 | 6.50 | 8.36 | 14.86 | 5.51 | 1.13 | •95 |

12 | 88.5 | 459 | 4.24 | 8.83 | 4.55 | .92 | •71 |

12 | 60 | 2.87 | 3.07 | 5.94 | 4.56 | •74 | .62 |

10 | 60 | 3.56 | 2.43 | 5.99 | 3.92 | .84 | •75 |

10 | 49 | 2.67 | 2.22 | 4.89 | 3.89 | .69 | .64 |

9 | 54 | 2.97 | 2.43 | 5.40 | 3.45 | .68 | .67 |

9 | 37 | 1.81 | I.9I | 3.72 | 3.43 | •59 | •55 |

8 | 43 | 2.28 | I.97 | 4.25 | 3.06 | •71 | .60 |

8 | 30 | 1.34 | 1.62 | 2.96 | 3.09 | .60 | •50 |

7 | 41 | 2.30 | I.80 | 4.10 | 2.68 | .65 | .65 |

7 | 26 | I.38 | 1.26 | 2.64 | 2.64 | .58 | .48 |

6 | 33 | 2.04 | 1.25 | 3.29 | 2.36 | .67 | .66 |

6 | 23 | I.09 | 1.18 | 2.27 | 2.27 | • 51 | .46 |

5 | 27.3 | I.69 | I.04 | 2.73 | 1.93 | .56 | .61 |

5 | 19 | .91 | •97 | 1.88 | 1.88 | •45 | .42 |

4 | 21.5 | 1.34 | .81 | 2.15 | 1.55 | .50 | •53 |

4 | 17.5 | 1.02 | •73 | 1.75 | 1.54 | .48 | •45 |

3 | 15 | .86 | .66 | 1.52 | 1.16 | .46 | •51 |

2 1/4 | 11.3 | .69 | •44 | 1.13 | .85 | •43 | .46 |

2 | 8.75 | •55 | •33 | .88 | •74 | •31 | •37 |

Note. - This chapter on struts is based upon the results of several hundred experiments conducted at the Pencoyd Iron Works.

The quality of the wrought iron was about as follows: elastic limit, 32,000 pounds per square inch; ultimate tensile strength, 49,600 pounds per square inch; ultimate elongation, 18 per cent in 8 inches.

The length of the specimens varied from 6 inches to 16 feet, and the ratio of length to least radius of gyration varied from 20 to 480.

For more detailed information, refer to articles by Mr. James Christie published in the Transactions of the Am. Soc. of Civil Engineers, entitled "Experiments on the Strength of Wrought-iron Struts".

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