One angle 2§ X 25 X j in. gives a net area of 1.19 — 0.20 = 0.99 sq. in., which is satisfactory. Compression Members. — Member MN having a length of 11 ft. 6 ins. carries 19,200 lbs. in compression. If the maximum ratio of length to least radius of gyration is 125 then the least radius of gyration is length divided by 125 or ||| = 1.10. The smallest angles that will serve are 3I ins. X 2 \ ins. Xj in., the long legs back to back, and separated f in. Their area is 2.88 sq. ins. According to the straight-line formula the allowable stress is p = 16,000 — 70- = 7250 lbs. The total load is 7250 X 2.88 = 20,900 lbs. This, being slightly in excess of the 19,200 lbs. stress in the member, is satisfactory. Compression members, JK, KL and the corresponding ones on the other side of the truss have the same load of 8000 lbs. and are approximately 84 ins. long. The least radius of gyration is its = 0.°7- The smallest angles are 25 ins. X 2 ins. X \ in., being also the smallest ordinarily permitted in this class of work. That is, no leg containing rivets shall be less than i\ ins. and no material t hall be less than \ in. thick. The minimum radius of gyration for / 84. the angle is 0.79 and the - value for this member is = 106. r 0.79 The allowable stress is p = 16,000 — 70 - = 8580 lbs. The total load on the section is 2 X 1.07 X 8580 = 18,400 lbs. Although this greatly exceeds the load on the member it is the smallest permitted by the specifications and will be used. The Upper Chord or Rafter. — The distance between apices along this chord is approximately 8 feet. The piece is subjected to combined compression and flexure. It will be assumed that purlins are spaced 6 ft. 0 ins. center to center and that the maximum bending will occur when a purlin lies midway between two adjacent apices. The load carried by each purlin is 6 X 25 X 34 = 5100 lbs. Considering the continuity and the method of securing it at the points of support it is usually safe to take the bending as fiveeighths of that on a beam similarly loaded but supported at the ends. The bending on a section of the upper chord whose span is 84 ins. is c iv r e M = § X . . = * X (5100 X 84) + 4 = 67,000 in. lbs. 048 The maximum compression along the upper chord is 90,000 lbs. and occurs in CJ. The design will be carried out for this member. The proper section can only be determined by trial, that is, a section must be assumed and then tested by cal- 1— culation to see if it satisfies the conditions. The section most frequently used is that shown in Fig. 170. The plate is —i U generally taken of sufficient width so that FlG the members joining the upper chord may be riveted directly to it. The section to be tried will be made up of two 4 in. X 3 in. X iVin. angles and one 10 X iVinplate. It is first necessary to find the center of gravity. Me The fiber stress due to bending is given by / = —. /„ = 67,000 X = 2800 lbs. Compressive stress. {, = 67,000 X = 8080 lbs. Tensile stress. The extreme fiber stress at backs of angles is — 12,300 — 2800 = — 15,100 lbs. The extreme fiber stress at edge of plate is —12,300 + 8080 = —3920 lbs. The radius of gyration of the section about the axis through the center line of the plate must now be found. Since r = \/t * A the inertia must be found first. The inertia of two angles about the axis parallel to the short legs is 2 X 3-38 = 6.76 The AW portion is 2 X 2.09 (1.26 + 0.16)' = 8.36 / = 16,000 — 70- = 16,000 — (70 X 60) = 11,800 lbs. Since wind and all other external forces have been considered this allowable fiber stress can be increased 25 per cent, making/ = 14,800 lbs. This being within 5 per cent of the stress estimated as acting in the piece, the 15,100 lbs. fiber stress can be allowed. Columns When knee braces are omitted the building must be stiffened in some other way. This may be done by designing the columns to withstand the wind loading in each panel on the side of the building, by designing the lateral bracing to carry all wind pressures to the ends or by assuming a division of this loading between the columns and the bracing. Actually the columns and bracing always share such loads, but as the proportion carried by each depends upon their relative stiffness the actual loading becomes a matter of considerable uncertainty. Just what assumptions are best to make will depend upon the length and height of the building, the assumed wind pressure, the manner of securing the tops of the columns to the trusses and the bases of the columns to the foundations. The assumptions for the design will also depend upon the judgment of the designer. All bracing should be given an initial stress when erected, to insure its acting promptly when the loading comes upon it. The portion of the column above the crane girder carries the roof load and will be liable to buckle about an axis parallel to the web. The load is applied concentrically to the column. There may be bending on the column about this axis from wind pressure on the end of the building, and from thrust due to the crane stopping and starting on its runway which should also be considered. Below the crane girder the inside angles of the column must transfer the crane load, including impact, to the full section of the column. As this transfer will occur in a short distance the r value may be neglected, hence the angles on this side of the column would require a minimum section of —'- = 4.13 sq. 16,000 ins. The two 6 in. X 3^ in. X iVin. angles used give an area of 5.78 sq. ins. and should prove ample. The roof load and the side of the building carried by the columns being both eccentric to the axes of the columns will produce bending on them. The resultant of these two loads and the crane load will most likely be eccentric to the center of gravity of the columns and will, therefore, produce a bending moment upon them. In addition to these the transverse thrust from the crane and the wind load on the side of the building will produce bending on the columns about an axis at right angles to the web. The effect of these moments will be materially reduced by the restraint at the column bases if the columns are fixed at that point. The maximum fiber stress resulting from the combination of direct and flexural stresses should not exceed that permitted upon the column when the maximum allowable stress has been reduced by a suitable column formula. Considering that the stresses are the resultant of wind load, crane load and dead load this reduced value may be increased 25 per cent. The column section below the crane girder must also be designed for a possible buckling about an axis parallel to the web, and for bending due to the crane thrust and wind load on the end of the building. The reactions at the tops of the columns are assumed as carried to the ends of the building by the lateral trusses in the lower chords of the roof trusses. As members of the lower chords of the roof trusses form parts of the lateral bracing such members should be examined to see that they will carry these bracing stresses in addition to those already on them from the truss load. The arrangement of the bracing is shown in Fig. 171. |