The following table, taken from Trontwine's handbook, may be used in estimating approximately the total loads on rooftrusses up to 75 feet span; the principals or trusses are supposed to be spaced 7 feet apart, centre to centre.

For spans from 75 to 150 feet, it will suffice to add 4 lbs. to each of the above total loads.

The above total loads may be considered to act vertically, and a reciprocal diagram similar to those obtained for the dead load may be drawn to determine the stresses and the dimensions of the various members, from which the weight of the truss or principal may be calculated. The weight thus obtained may be used in estimating the dead loads for the complete calculations.

In Chapter III., two methods were considered for determining the stresses in braced structures, which were illustrated with reference to the common roof-truss shown in Fig. 125. The stresses in this roof will now be more fully considered, and, in the first place, the results obtained in Chapter III. may be tabulated thus

With regard to the stresses due to wind :

If a horizontal force of wind of 50 lbs. per square foot act upon one side of the roof, the normal pressure due to this force may be obtained from Table LXIX., p. 286.

The angle of the roof is 2210, so that the normal pressure is

25 lbs. per square foot.

Since the roof principals are 12 feet apart centre to centre, and the length of the rafters is 21.6 feet, the total wind force on one side acting normally to the roof is

12 × 21.6 × 25 = 6480 lbs.

If the roof principal is bolted down at each shoe, so that the ends are fixed, the stresses may be obtained by measuring the

reciprocal diagram, Fig. 127. The results are given in the following table, compared with those obtained by the method of moments, thus:

We see that if the wind is on the left, the bar DE is unstressed; if the wind is on the right, AB is unstressed.

The direction of the reactions R1 and R2 is normal to that of the principal rafter, and the values of these reactions may be determined by means of the polar and funicular polygons shown in dotted lines, Figs. 127 and 125. The point z is determined by drawing the line oz parallel to the closing line in the funicular polygon.

If one end of the principal is fixed, and the other end is free to move on expansion rollers, the principal will tend to expand or contract when the temperature changes, motion taking place as soon as the forces due to changes of temperature are sufficient to overcome the frictional resistance of the expansion rollers. When the frictional resistances just balance the forces due to temperature, the whole of the horizontal component of the wind pressure must be resisted by the fixed end, since the roller end can only supply a vertical reaction.

The vertical components of the normal reactions at the fixed and free ends remain the same as in the case last considered. Two cases require to be considered, namely, the wind on the left and the wind on the right (Figs. 128 and 129); wind on the left with the left end free to move (Fig. 128).

The diagram obtained for this case differs slightly from Fig. 127, as the horizontal component of the reactions at both ends.

must be entirely supplied by the fixed end. The stresses are given in the following table :

TABLE XXVIII.

STRESSES DUE TO WIND ON LEFT, LEFT END MOVABLE.

Wind on the right, with the left end movable. The stresses due to this case may be tabulated in a similar manner to the foregoing, thus

TABLE XXIX.

STRESSES DUE TO WIND ON RIGHT, LEFT END MOVABLE.

The details of the calculations by the method of moments is left for the student to verify.

The maximum stresses on any member of the truss due to wind may be obtained from an inspection of the foregoing tables. The resultant stress is found by combining the maximum wind stress with the dead-load stress, thus

TABLE XXX.

TABLE OF MAXIMUM STRESSES DUE TO DEAD LOAD AND WIND PRESSURE.