US1919405A - Truss - Google Patents

Description

W. H. WILSON .Fufiy 25, 1933.

TRUSS Filed April 16, 1928 IN {VTO H Zw/V;

ATTORNEYS.

patented July 25, 1933 UNITED STATES WILLIAM H. WILSON, OF LOS ANGELES, CALIFORNIA TRUSS Application filed April 16,

This invention relates to steel trusses, and more particularly to steel trusses suitable for floor and roof construction of buildings, which are commonly called trussed steel joists.

The object of the invention is to obtain economy in the top chords of the joists. These top chords are required to resist a combination of compressive stresses made up of the compression which is usual in the top chord of an truss and also a compression in part of the bers which is caused by the resistance to bending due to the uniform load resting upon the top chord in between the panel points. As the load on these steel joists is always applied uniformly throughout the length of the joists and is not applied at panel points, as is customary where the joists are spaced at considerable distances apart and the 29 loads are placed upon them by purlins running between them, the top chord must act as a beam between the panel points.

In the drawing:

Figure 1 represents a side elevation of a steel joist with ends resting on steel beams and supporting a concrete floor slab of uniform thickness, and v Figure 2 represents a section through the joist and shows the construction of the top chord which in this particular case is a structural steel T, also the construction of the other members of the truss.

Referring now with particularity to the drawing, the improved truss is designated as an entirety by A, and in the present embodiment such truss includes a top chord a, a bottom chord b with struts or webs c extending between the top and bottom chords, and diagonals d secured for bracing purposes between the top and bottom chords. The truss may be supported upon suitable beams, shown at e and f, and the bottom chord member inclines vupwardly at ends of the truss where the truss is supported upon the beams. I may, if desired, provide either a ceiling or a flooring, as the case may be, on the top chord,

as shown at g.

The truss illustrated is particularly adapted for building purposes and it will be observed that the panel points vary as to width it augments the compressive stress previously 1928. Serial No. 270,416.

of section. The spacing between the top and bot-tom chord is substantially uniform but the spacing between the diagonals which would constitute a panel varies from the center strut 1 toward the beams e and f. It will be noted, for instance, that the spacing between the strut 1 and the strut 2 is a certain distance apart while the distances between strut 2 and 3, and 3 and 4, and t to the beam 6 are all of dilferentlength. This is done for a particular reason, as will hereinafter appear, the main reason for the construction being to so arrange the lengths of the panels that the compression stress due to bending is a minimum where the direct compression stress is a maximum, and is a maximum Where the direct compression stress is a minimum so that the total combined stresses for which the panel must be designed is practically uniform throughout the entire length of the joist.

Any suitable means may be utilized for securing the diagonals to the bottom and top chords, such as by welding, as shown at 5, or by riveting, as the case maybe.

As -in all trusses, the top chord is subjected to direct compression stress caused by the load put upon the truss. If the loads were applied directly at the panel'points, this would be the only stress to which the top chord is subjected but in the case of all steel joists the load is applied uniformly throughout the length of the joist,as indicated in the drawing. Therefore, there is a second set of stresses developed in this top chord due to the tendency of it to bend in between the panel points because of the load placed upon it between the panel points. As in the case of all beam bending, this stress due to bending is of two kinds, part being a tensile stress and part being a compressive stress. Naturally the tensile stress can be disregarded as itmerely tends to offset the direct compression stress previously referred to, but the com ressive stress due to bending must be consi ered as referred to. Considering each section of the top chord between intersections of web members as a simple beam, the maximum moment will occur at the center of the distance between the intersection of the Web members and the maximum compression will occur at the top of the chord section.

In order to demonstrate the advantage of my invention it is necessary to analyze and set forth these two compressive stresses.

Referring to the drawing, the following assumptions are made: Distance center to center of I-beam supports 320; depth of steel joist over all 20 effective depth of steel joist 19"; total load on steel joist 100 pounds per lineal foot uniformly applied; size of top chord T, flange 3 by .29, total depth of stem 2% tapering from 3: 1; at bottom to A at shank; distance from top of T to neutral axis .572; distance from bottom of T to neutral axis 1.928; section modulus of T about horizontal axis is 336'; area of T equals 1.35 square inches.

If all of the panels are of equal length, they will be 4'0 and the load at each panel point will be 400 pounds and the reaction at each end will be 1400 pounds.

The direct compressive stress in the top chord in any panel is obtained by taking moments about a point in that panel, reducing such moment to inch pounds and dividing the quantity by the efi'ective depth of the truss in inches. The quotient represents the compression stress in the top chord in pounds. In this way, it will be found that the direct compressive stresses in the top chord throughout the truss are as follows :1

Pounds per square inch First panel 2622 Second panel 4496 Third panel 5607 Center panel 5978 If each of the panels is of equal length necessarily the bending moment due to the application of the load uniformly between the panel points will be equal for all panels and is equal to one-eighth of W1 where W equals the total load and 1 equals length in inches. The moment, therefore, is equal to 400x48 divided by 8, or 2400 inch pounds. According to the formula.M divided by s is equal to f where M equals bending moment in inch pounds, sequals section modulus and 7'' equals the maximum extreme fibre stress in pounds per square inch. The fibre stress in this case will be equal to 2400 divided by .336 or 7143 pounds per square inch. This, however, is the stress at the extreme fibre and is therefore a tensile stress, as the distance from the neutral axis to the extreme part of the T which is in tension is greater than the distance from the neutral axis to the extreme part of the T which is in compression. The stresses vary from 0 at the neutral axis to a maximum at the extreme fiber and the stress at any point is therefore directly proportional to its distance from the neutral axis. The maximum compression stress in this case will therefore bear the same relation to the maximum tensile stress found above as the distance from the top of the T to the neutral axis bears to the distance from the bottom of the T to the neutral axis. Therefore, the compression stress is equal to 7143 multiplied by .572 and divided by 1.928, or 2119 pounds per square inch.

Adding these stresses to the compressive fibre stress due to bending of 2119 pounds per square inch, we get total compressive fibre stresses as follows:

Pounds per square inch First panel 4741 Second panel 6615 Third panel 7726 Center panel 8097 per square inch First panel 3333 Second panel -Q 4993 Third panel 5760 Center panel 6020 and the compression stresses due to bending are as follows:

Pounds per square inch First panel Second panel 2200 Third panel 1560 Center panel 1270 Adding these together, the total compression stresses are t en as follows:

Pounds I per square inch First panel 123 Second panel 7193 Third panel 7320 Center panel 7290 the total span and the depth. They are, however, uniform for any one joist except as small variations are made in the length of the end panels to allow for slight variations in the total span of the joists, but not for the purpose of economy in design.

Referring to the rst set of combined stresses, it will be seen that the total stress low sign the top chord for the maximum stresses and it is, therefore, evident that the top chord is only working to capacity for a very small panel it is only Working to slightly more than 50% of its total strength.

This condition has, of course, always been known to engineers and in structural steel construction it is provided for either by splicing the top chord at two or more of the panel points and using smaller sections for the reduced compression stresses or by using a continuous member for the top chord sufficient to take care of the stresses at. or near the end and reinforcing it to carry the heavier stresses at the center by the addition of plates or angles. In steel joist construction, however, the joists are spaced closely together involving great duplication and must, therefore, be of such simple construction as to alof quantity production methods in their manufacture. Furthermore, the top surface of the joist must be uniform so as to provide a uniform bearing for. the floor construction which the joists support. It is, therefore, evident that it is impractical to employ the methods of splicin or reinforcing described, or any other metho s which might be used for ordinary steel truss construction.

Referring to the second set of figures, it will be seen that the total stress is almost uniform throughout the entire length of the joist.

is means that a uniform section may be used throughout the entire length of the joist and that it will be working at almost 100% capacity throughout its entire length. This, of course, must result in economy and a comparison of the total stresses shows that in the first case the top chord must be designed for 8097 pounds per sq. inch and according to my invention for only 7320 pounds per sq. inch. This means ,that the section used in the first case must be approximately 10% larger than that used when by invention is applied.

The sizes of the bottom chord and of the web members in both cases would be substantially the same and as the number of pieces to be handled is the same, it is apparent that there is considerable economy obtained by my method. percentage of its total length and in the end A similar comparison could be drawn had I chosen for demonstration a joist With more or less panels. A larger number produces smaller panels and reduces the compression stress due to bending, and fewer panels have the reverse eflect but the comparative economy remains substantially the same.

It is obvious that various changes may be made in practicing the invention relative to the method of bracing of the joist as well as the number of panel points, and that the features and the inventlve concept may be used for other purposes than for joists, such as in bridges and the like.

'Having thus described my invention, what I claim and desire to secure by Letters Patent is:

A steel joist, adapted to support a load uniformly distributed throughout its length, comprising a top and a bottom chord member and web members therebetween and intersecting the same and dividing the said top chord into panels; the number of panels and their lengths being symmetrical about the center line of the joist and the lengths of the anels being a minimum at the'center and eingincreased in length progressively from the center to the ends of the joist, said increases in length being such that the compressive fibre stress, due to local bending in each top chord panel is increased, due to longer panel length, by substantially the same amount as the direct compressive fibre stress is reduced in said panel dueto its distance from the center line of the joist, whereby the total combined compressive fibre stress in the top chord member is substantially uniform throughout the entire length of the joist.

WILLIAM H. WILSON.

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