This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.

In practice, spans not exceeding twenty times the flange width are not considered to require side support.

In some cases there must be made still another modification of the loads indicated by these tables, and that is to provide against excessive vertical deflection. It is well known that all members loaded transversely will bend before they will break. In other words, any given load causes a certain amount of deflection. It is not practicable, however, to allow this deflection to be very great in structural members, because of the resulting vibration and because where there are plastered surfaces cracks will occur. It is

Distance between Supports in Feet | 24" I | 20" I | 18" I | 15" I | 12" I | 10" I | ||||

80 lbs. | 80 lbs. | 65 lbs. | 55 lbs. | 80 lbs. | 60 lbs. | 42 lbs. | 40 lbs. | 31.5 lbs. | 25 lbs. | |

12 | 128.9 | 108.6 | 86.6 | 65.5 | 78.6 | 60.1 | 43.6 | 33.2 | 26.6 | 18.1 |

13 | 109.8 | 92.6 | 73.8 | 55.8 | 67.0 | 51.3 | 37.2 | 28.3 | 22.7 | 15.4 |

14 | 94.7 | 79.8 | 63.7 | 48.1 | 57.7 | 44.2 | 32.1 | 24.4 | 19.6 | 13.3 |

15 | 82.5 | 69.5 | 55.5 | 41.9 | 50.3 | 38.5 | 27.9 | 21.3 | 17.1 | 11.6 |

16 | 72.5 | 61.1 | 48.7 | 36.8 | 44.2 | 33.8 | 24.5 | 18.7 | 15.0 | 10,2 |

17 | 64.2 | 54.1 | 43.2 | 32.6 | 39.2 | 30.0 | 21.7 | 16.5 | 13.3 | 9.0 |

18 | 57.3 | 48.3 | 38.5 | 29.1 | 34.9 | 26.7 | 19.4 | 14.8 | 11.8 | 8.0 |

19 | 51.4 | 43.3 | 34.6 | 26.1 | 31.3 | 24.0 | 17.4 | 13.2 | 10.6 | 7.2 |

20 | 46.4 | 39.1 | 31.2 | 23.6. | 28.3 | 21.7 | 15.7 | 12.0 | 9.6 | 6.5 |

21 | 42.1 | 35.5 | 28.3 | 21.4 | 25.7 | 19.6 | 14.2 | 10.8 | 8.7 | 5.9 |

22 | 38.4 | 32.3 | 25 8 | 19.5 | 23,4 | 17 9 | 13 0 | 9.9 | 7 9 | 5.4 |

23 | 35.1 | 29.6 | 23.6 | 17.8 | 21.4 | 16.4 | 11.9 | 9.0 | 7.3 | 4.9 |

24 | 32.2 | 27.2 | 21.7 | 16.4 | 19.6 | 15.0 | 10.9 | 8.3 | 6.7 | 4.5 |

25 | 29.7 | 25.0 | 20.0 | 15.1 | 18.1 | 13.9 | 1.0 1 | 7.7 | 6.1 | 4.2 |

26 | 27.5 | 23.1 | 18.5 | 13.9 | 16.7 | 12.8 | 9.3 | 7.1 | 5.7 | 3.9 |

27 | 25.5 | 21.5 | 17.1 | 12.9 | 15.5 | 11.9 | ft 6 | 6.6 | 5 3 | 3.6 |

28 | 23.7 | 20.0 | 15.9 | 12.0 | 14.4 | 11.0 | 8.0 | 6.1 | 4.9 | 3.3 |

29 | 22.1 | 18.6 | 14.8 | 11.2 | 13.5 | 10.3 | 7.5 | 5.7 | 4.6 | 3.1 |

80 | 20.6 | 17.4 | 13.9 | 10.5 | 12.6 | 9.6 | 7.0 | 5.3 | 4,3 | 2.9 |

Distance between Supports in Feet | 9" I | 8" I | 7" I | 6" I | 5" I | 4" I | 3" I |

21 lbs. | 18 lbs. | 15 lbs. | 12.25 lbs. | 9.75 lbs. | 7.5 lbs. | 5.5 lbs. | |

5 | 80.5 | 60.7 | 44.2 | 31.0 | 20.6 | 12.7 | 7.0 |

6 | 55.9 | 42.1 | 30.7 | 21.5 | 14.3 | 8.8 | 4.9 |

7 | 41.1 | 31.0 | 22.5 | 15.8 | 10.5 | 6.5 | 3.6 |

8 | 31.5 | 23.7 | 17.3 | 12.1 | 8.1 | 5.0 | 2.8 |

9 | 24.9 | 18.7 | 13.6 | 9.6 | 6.4 | 3.9 | 2.2 |

10 | 20.1 | 15.2 | 11.1 | 7.8 | 5.2 | 3.2 | 1.8 |

11 | 16.6 | 12.5 | 9.1 | 6.4 | 4.3 | 2.6 | 1.5 |

12 | 14.0 | 10.5 | 7.7 | 5.4 | 3.6 | 2.2 | 1.2 |

13 | 11.9 | 9.0 | 6.5 | 4.6 | 3.1 | 1.9 | 1.0 |

14 | 10.3 | 7.7 | 5.6 | 4.0 | 2.6 | 1.6 | 0.9 |

15 | 9.0 | 6.7 | 4.9 | 3.4 | 2.3 | 1.4 | |

16 | 7.9 | 5.9 | 4.3 | 3.0 | 2.0 | 1.2 | |

17 | 7.0 | 5.3 | 3.8 | 2.7 | 1.8 | 1.1 | |

18 | 6.2 | 4.7 | 3.4 | 2.4 | 1.6 | .98 | |

19 | 5.6 | 4.2 | 3.1 | 2.2 | 1.4 | ||

20 | 5.0 | 3.8 | 2.8 | 1.9 | 1.3 | ||

21 | 4.6 | 3.4 | 2.5 | 1.8 | 1.2 | ||

22 | 3.8 | 3.1 | 2.3 | 1.6 | 1.1 |

For load of 200 pounds per square foot, divide the spacing given by 2. Maximum fibre stress, 16,000 pounds per square inch. For spacings above the dotted line, the safe loads for bending are greater than the safe loads for web crippling, as explained on page 255.

Distance between Supports in Feet | 24" I | 20" I | 18" I | 15" I | 12" I | 10" I | ||||

80 lbs. | 80 lbs. | 65 lbs. | 55 lbs. | 80 lbs. | 60 lbs. | 42 lbs. | 40 lbs. | 31.5 lbs. | 25 lbs. | |

12 | 85.9 | 72.4 | 57.7 | 43.7 | 52.4 | 40.1 | 29.1 | 22.1 | 17.7 | 12.1 |

13 | 73.2 | 61.7 | 49.2 | 37.2 | 44.7 | 34.2 | 24.8 | 18.9 | 15.1 | 10.3 |

14 | 63.1 | 53.2 | 42.5 | 32.1 | 38.5 | 29.5 | 21.4 | 16.3 | 13.1 | 8.9 |

15 | 55.0 | 46.3 | 37.0 | 27.9 | 33.5 | 25.7 | 18.6 | 14.2 | 11.4 | 7.7 |

16 | 48.3 | 40.7 | 32.5 | 24.5 | 29.5 | 22.5 | 16.3 | 12.5 | 10.0 | 6.8 |

17 | 42.8 | 36.1 | 28.8 | 21.7 | 26.1 | 20.0 | 14.5 | 11.0 | 8.9 | 6.0 |

18 | 38.2 | 32.2 | 25.7 | 19.4 | 23.3 | 17.8 | 12.9 | 9.9 | 7.9 | 5.3 |

19 | 34.3 | 28.9 | 23.1 | 17.4 | 20.9 | 16.0 | 11.6 | 8.8 | 7.1 | 4.8 |

20 | 30.9 | 26.1 | 20.8 | 15.7 | 18.9 | 14.5 | 10.5 | 8.0 | 6.4 | 4.3 |

21 | 28.1 | 23.7 | 18.9 | 14.3 | 17.1 | 13.1 | 9.5 | 7.2 | 5.8 | 3.9 |

22 | 25.0 | 21.5 | 17.2 | 13.0 | 15.6 | 11.9 | 8.7 | 6.6 | 5.3 | 3.6 |

23 | 23.4 | 19.7 | 15.7 | 11.9 | 14.3 | 10.9 | 7.9 | 6.0 | 4.9 | 3.3 |

24 | 21.5 | 18.1 | 14.5 | 10.9 | 13.1 | 10.0 | 7.3 | 5.5 | 4.5 | 3.0 |

25 | 19.8 | 16.7 | 13.3 | 10.1 | 12.1 | 9.3 | 6.7 | 5.1 | 4.1 | 2.8 |

2G | 18.3 | 15.4 | 12.3 | 9.3 | 11.1 | 8.5 | 6.2 | 4.7 | 3.8 | 2.6 |

27 | 17.0 | 14.3 | 11.4 | 8.6 | 10.3 | 7.9 | 5.7 | 4.4 | 3.5 | 2.4 |

28 | 15.8 | 13.3 | 10.6 | 8.0 | 9.6 | 7.3 | 5.3 | 4.1 | 3.3 | 2.2 |

29 | 14.7 | 12.4 | 9.9 | 7.5 | 9.0 | 6.9 | 5.0 | 3.8 | 3.1 | 2.1 |

30 | 13.7 | 11.6 | 9.3 | 7.0 | 8.4 | 6.4 | 4.7 | 8.5 | 2.9 | 1.9 |

Distance between Supports in Feet | 9" I | 8" I | 7" I | 6" I | 5" I | 4" I | 3" I |

21 lbs. | 18 lbs. | 15 lbs. | 12.25 lbs. | 9.75 lbs. | 7.5 lbs. | 5.5 lbs. | |

5 | 53.7 | 40.5 | 29.5 | 20.7 | 13.7 | 8.5 | 4.7 |

6 | 37.3 | 28.1 | 20.5 | 14.3 | 9.5 | 5.9 | 3.3 |

7 | 27.4 | 20.7 | 15.0 | 10.5 | 7.0 | 4.3 | 2.4 |

8 | 21.0 | 15.8 | 11.5 | 8.1 | 5.4 | 3.3 | 1.8 |

9 | 16.6 | 12.5 | 9.1 | 6.4 | 4.3 | 2.6 | 1.5 |

10 | 13.4 | 10.1 | 7.4 | 5.2 | 3.4 | 2.1 | 1.2 |

11 | 11.1 | 8.3 | 0.1 | 4.3 | 2.8 | 1.8 | 1.0 |

12 | 9.3 | 7.0 | 5.1 | 3.6 | 2.4 | 1.5 | 0.8 |

13 | 7.9 | 6.0 | 4.4 | 3.1 | 2.0 | 1.3 | |

14 | 6.9 | 5.2 | 3.8 | 2.6 | 1.8 | 1.1 | |

15 | 6.0 | 4.5 | 3.3 | 2.3 | 1.5 | 0.9 | |

16 | 5.2 | 4.0 | 2.9 | 2.0 | 1.4 | ||

17 | 4.7 | 3.5 | 2.6 | 1.8 | 1.2 | ||

18 | 4.1 | 3.1 | 2.3 | 1.6 | 1.1 | ||

19 | 3.7 | 2.8 | 2.0 | 1.4 | 1.0 | ||

20 | 3.4 | 2.5 | 1.8 | 1.3 | |||

21 | 3.0 | 2.3 | 1.7 | 1.2 | |||

22 | 2.8 | 2.1 | 1.5 | 1.1 |

For load of 300 pounds per square foot, divide the spacing given by 2. Maximum fibre stress. 16,000 pounds per square inch. For spacings above the dotted line, the safe loads for bending are greater than the safe loads for web crippling, as explained on not sufficient, therefore, merely to get a section strong enough to carry the given load, it must also be stiff enough not to deflect more than a certain proportion of its length under this load. It has been determined that a beam can deflect 1/360 of its length, or 1/30 of an inch per foot of length, without causing cracks in a plastered ceiling; and it is this criterion which is generally followed in determining the section required to meet the condition of safe deflection.

In Table I the loads above the heavy black line are the safe loads which can be carried without exceeding the above deflection. A beam may be used on spans longer than those above the black line; but in this case, in order not to exceed the safe deflection, the load indicated by the tables opposite this span must be reduced by the following rule:

Rule for Safe Loads above Spans Limited by Deflection. Divide the load given opposite the span corresponding to the length of beam by the corresponding span, and multiply by the span given just above the black line; or,

If S2 = the given span,

L = the tabular load for this span,

S21 = the span just above the heavy black line,

L1 = the required load, then L1 = S21L/S2

In cases where the depth of beam is not limited, comparison of different depths of beams should be made, and the one selected which proves the most economical.

Spacing of Beams. In many cases where the location of columns and spacing of beams are not fixed by certain features of design or construction, the problem arises in a form for which a table different from Table I is more useful. For instance, if the problem is to space the columns and beams to give the most economical sections to carry the given loads, Table II will be useful. This gives the spacing of beams for different spans to carry safely a load of 100 lbs. and 150 lbs. per square foot. By comparisons, therefore, of the different sections, spans, and spacing that may be used, the most economical section can be selected.

The above table is useful also when it is desired to know the loading that a certain floor was designed to carry and when only the framing plan is at hand.

If other loads per square foot are used, the table can be modified by dividing the spacings given by the ratio of the required load to the indicated load of the table. The same modifications for lateral and vertical deflection must be made as in the preceding table.

In all cases where there is a choice between beams of different depths, it should be borne in mind that beams of greater depth than 15 inches cost an extra one-tenth of a cent per pound; this, therefore, affects their relative economy.

Deflection. As noted in preceding paragraphs, it is important to know what the vertical deflection of a shape will be under the loads and for the spans specified, as in the majority of cases the section cannot be selected from the tables of safe loads because of unequal loading or because some other shape is used. It is therefore necessary to be able to calculate from additional tables what the deflection will be.

The following formula can be readily used for this purpose. We shall first explain its derivation.

The general formula for the deflection of any shape supported at the ends and loaded uniformly is: d = 5 Wl3 / 384 EI

Where W is the total load, E the modulus of elasticity, and

I the moment of i nerti a. 5

.--------is a constant since E = 29,000,000

W = pl, and M = 1/8pl2 =1/8 Wl and M = I = Wl ; therefore Wl = 8x16,000xI f y 8 X 16,00 y if the beam is loaded up to its full capacity, and the fibre stress is taken at 16,000.

Therefore d = 5l2x8x16,000xI / 384 EI y

=.0000575l2 / y (1), or, since h = depth of beam = 2y,

= .000115l2 / h (2).

In this formula I must be taken in inches.

From this general formula (1) a table in a number of different forms can be made. In Table III different values of I are substituted, so that the deflection in inches is obtained by taking the constant in the table corresponding to the given span, and dividing by the depth of the beam.

Another table could be made by substituting different values of h corresponding to different beams, and this would readily give for each beam the deflection by multiplying by the square of the span in inches.

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