The condition of the stress borne by a Girder is that of a beam fixed or supported at both ends, as the case may be, supporting the weight borne by all of the beams resting thereon, at the points at which they rest; and its dimensions must be proportionate to the stress upon it, and the distance between its points of insertion or support.

Illustration

It is required to determine the dimensions of a pitch-pine girder, 16 feet between its several points of supports, to support the ends of two lengths of beams each 20 feet in length, having a superincumbent weight, including that of the beams, of 200 lbs. per square foot.

The condition of the stress upon such a girder would be that of a number of beams, 40 feet in length (20x2), supported at both ends, and loaded uniformly along their length, with 200 lbs. upon every superficial foot of their area.

Hence the amount of the weight to be borne is determined by 20x2X 15X200=120,000 lbs.= the product of twice the length or a beam, the distance between the supports of the girder and the weight borne per square foot of area; and the resistance to be provided for is that to be borne by a beam, 15 feet in length, fixed at both ends, and supporting 120,000 lbs. uniformly laid along its length, equal to 60,000 lbs. supported at its centre.

15x60,000

Consequently,------------= 3000=quotlent of the product of the length

6X50 and weight -:- the product of 6 times the value of the material: and assuming the girder to be 12 inches wide, then √ 3000 / 12 =15.8 ins.

• When a girder has four or more supports, its condition as regards a stress upon its middle is that of a beam fixed at both ends.

Formulae To Compute The Values And The Dimensions Of Beams, Bars, Etc., Of Various Sections. - (Tredgold.)

For a Square, Rectangle, Rectangle the diagonal being vertical, and Cylinder, they are alike to those already given, substituting in the Rectangles for b d2. S3.

For a Grooved or Double-flanged, Open, and Single-flanged Beam they are as follows:

Grooved.

Open.

Formulae To Compute The Values And The Dimensions 53

Formulae To Compute The Values And The Dimensions 54

1. Fixed at one End,] Weight suspended from the other,

lw / b d² (l-q y³) =V.

lw / b d² (l-y³) = V.

2. Fixed at both Ends,' Weight suspended from the middle,

lW / b d² (l-qy³) = V.

lW / b d² (l-y³) = V.

3. Supported at both' Ends, Weigh suspended from the middle,

lW / b d² (l-y³) = V.

lW / b d² (l-y³) = V.

4. Supported at both Ends, Weight suspended at any other point than the middle,

_____ m n W / b d² m + n (l-q y³ ) = V.

_____ m n W / b d² m + n (l-y³ ) = V.

5. Fixed at both Ends, Weight suspended from any other p't than the middle,

_____ m n W / b d² m + n (l-q y³ ) = V.

_____ m n W / b d² m + n (l-y³ ) = V.

Formulae To Compute The Values And The Dimensions 55

Single-flanged

1. { lw / b d² (l-q y³) (l-q)/ (√1-q y³

+ √1-q)² = V.}

For the other conditions of a Beam, Bar, etc., use the same formula as the above, multiplying the Value obtained above by 6, 4, 1 and 1.5 respectively, y and q depth of groove whole breadth of beam-representing--------------------------------=y, and------------------------------------whole depth of beam width of web whole breadth of beam.

------------------------------------=q.

Transverse Resistance From End Pressure Applied Horizontally

Transverse Resistance From End Pressure Applied Ho 56