31. In Figs. [28] and [29], the pull of one hoisting rope running from the top of the drum was considered, but in most cases it is necessary to consider the pull from two hoisting ropes, one running from the top and one from the bottom of the drum f, as shown in [Fig. 30]. a b and a′ b′ represent the directions of action of the two forces acting on the hoisting ropes, while the two vertical forces a c and a′ c acting down the shaft are approximately equal to the two forces acting toward the drum. There are, therefore, two resultants a d and a′ d′, the directions of which are determined by lines from a and a′ through the center of the sheave e. The amounts of these resultant forces can be determined by the parallelogram of forces as shown in Figs. 28 and 29. A resultant that is a mean between a d and a′ d′, both in position and amount, is sometimes taken, or the greater value as determined from a d or a′ d′ and the greatest inclination as given by a′ d′ may be used, as being the worst theoretical conditions to which the frame may be subjected. A head-frame usually has a vertical post approximately parallel to the vertical pull of the rope in the shaft, and an inclined member g h approximately parallel to the resultant determined by the parallelogram of forces. If g h, [Fig. 30], is parallel to the resultant, the vertical leg h i is under no strain and merely supports the end of g h. If the resultant falls between g h and h i, both of these legs will be under compression. If the resultant falls outside of g h, the leg g h will be under compression and h i will be under tension. The head frame will be most stable when the resultant falls between g h and h i, but this cannot always be accomplished in building the frame on account of the conditions at the head of the shaft; nor is it always advisable to do so from structural considerations.
32. Since wood is much better adapted to withstand compressive than tensile stresses and since steel is adapted to withstand either tensile or compressive stresses, it is much more important that the members of timber frame conform as closely as possible to the theoretical line worked out in Figs. 28, 29, and 30 than in the case of a steel frame. Take, for instance, the case shown in [Fig. 31], where for some local reason it is impossible to put an inclined strut in or near the line of the resultant stress to withstand the pull that tends to overturn the head-frame. In a steel structure, a can very easily be made a tension member by anchoring its lower end to a heavy foundation. This resists the tendency to overturn and makes a very stable structure. In practice, braces can generally be located parallel to the line of resultant strain, [Fig. 29], or outside this line, as shown in [Fig. 30], so that the strain due to the pull of the rope will come mainly on the inclined brace and not on the upright. To distribute the stress on the foot of the different parts of the frame, an inclined brace is usually set farther from the shaft than the parallelogram of forces locates it, and so placed that about two-thirds of the strain due to the pull of the rope comes on the brace and one-third on the upright parts of the frame. In order to give the frame a more stable base and because the base must be larger than the top of the frame to bring the foundations back from the shaft mouth, usually the members h i are also slightly inclined.
Fig. 31
Wherever permanency of head-frames is required, if steel is obtainable at a price at all comparable with wood, steel structures are being used, as timber frames rot.
TYPES OF HEAD-FRAMES
33. There are three types of head-frame construction—the A type, the square type without an inclined brace, and the square type with an inclined brace.
34. A Type of Head-Frame.—[Fig. 32] shows the construction of a triangular, or A-shaped, head-frame of which (a) is a side elevation and (b) an end view. This particular frame is largely used at anthracite mines, but the type is one quite commonly used for timber frames, though the details of construction vary in different localities. The height of the frame is from 30 to 50 feet, and with direct-acting engines this height should be sufficient to allow a play of at least two-thirds of a revolution between the cage landing and the overwinding point. The posts a are parallel to the hoisting rope b as it hangs down the shaft and the inclined brace c, which resists any thrust that would tend to rotate the head-frame, is parallel to the resultant pull of the two parts of this rope b; the inclined braces d stiffen the frame and help support the cross-timbers m that support the cage guides e. The sills f are made of three pieces of timber 8 inches by 14 inches in cross-section. The posts a rest in cast-iron shoes g that are firmly bolted to the posts and sills. The inclined braces c, d are fitted with cast-iron shoes h, i. The post a and the two braces c, d are held in place at the top of the frame by the casting j, which also supports the pillow-block k.
The posts a and the brace c are made up of two pieces of timber each 8 inches by 14 inches in cross-section. The brace d consists of one piece of timber 8 inches by 14 inches in cross-section. The transverse braces l consist of two pieces of timber 6 inches by 14 inches in cross-section, bolted through the timbers a and c. The supports m for the guides are single pieces of 8" × 8" timber. The center post, as shown in [Fig. 32 (b)], is braced by the two pieces n, o, which are supported by two timbers p, q bolted to the two outside posts. The posts a and the inclined braces c are further braced by the tie-rods r, s, t, and u, all of which are fitted with turnbuckles, as shown at v. The different posts are firmly bolted together, the bolts being fitted with cast-iron washers.
