Expansion roof
This application is a continuation of application Ser. No. 471,642 filed Mar. 3, 1983, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates generally to building structures, and more particularly to building structures having rafter framed roofs. 
     As is known in the art, building structures are often provided with multiple roof structures, having roofs of different elevations and pitches. Generally, in order to provide a roof structure for such a building, it is required to provide interior carrying beams and support columns for each one of such roofs at each one of such levels. While this solution is an adequate solution for many applications, it does unnecessarily increase the cost of the building by requiring the use of expensive support columns and load carrying beams to support each one of such roofs at each elevation level. Further, the use of support and carrying beams in such a structure present interior obstructions which restrict the size and layout of rooms. Further still, the amount of open space between the floor and the ceiling is likewise restricted by the use of interior support columns and load carrying beams restricting location of stairways and head room in stairways. Further still, in some buildings it is often desired to provide an atrium. An atrium is generally considered to be an aesthetically desirable feature in certain buildings such as large houses. However, with interior support columns and load carrying beams required to join roofs of different elevation and pitch, for example, construction of an atrium where the two roofs join is difficult. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, framing for a roof includes a first pair of divergently spaced members, each one of such members having a first end portion connected at a first common point, and a second pair of divergently spaced members, each one having a first end portion connected at a second common point. A second end portion of each one of such members of the first pair is colinearly aligned with a second end portion of a corresponding one of the second pair. A longitudinal member is connected between the common points of each of the connected pairs of members and a plurality of spaced rafter members is connected between corresponding ones of each of the pair of divergently spaced members. With such an arrangement, the framing for a roof is provided which eliminates the necessity for carrying beams and interior support columns providing an area of open living space adaptable to a wide range of room layouts. 
     In accordance with an additional aspect of the present invention, a roof structure for a building includes a first pair of hip rafters associated with a first roof, each hip rafter having a first end connected at a first common point, and having second end portions connected at first points with exterior walls of the building, and a second pair of hip rafters associated with a second roof, each hip rafter having a first end connected at a second common point, and each having a second end portion colinearly aligned with the second end portion of such first pair of hip rafters and connected at second points of the exterior walls of the building. A horizontal member is connected between the common points of each of said pair of hip rafters. A plurality of expansion rafters having selective compound angle cuts at ends thereof are then connected at spaced intervals between a corresponding one of pair of hip rafters. With this arrangement, an expansion roof structure is provided which eliminates the necessity for carrying beams and interior support columns thereby providing an area of living space adaptable to a wide range of room layouts. Further, since the carrying beams and support structures generally associated with prior roofing structures are eliminated, an atrium entrance way effect is provided resulting in an unobstructed view of the entire interior area. 
     In an alternate embodiment of the present invention, each one of pairs of expansion roof rafters include selectively tapered longitudinally beveled surface portions which provide a curved centerline. The tapered, beveled surface and hence the curved centerline are determined by the pitch of each one of the expansion rafters. A plurality of selectively tapered sheathing is fastened across the tapered, beveled surface of each one of the rafters. With this arrangement, a roof structure is provided with the sheathing being gradually elevated and pitched from a lower portion to an upper portion following the individual pitches of each one of the expansion rafters, and thus permitting roofs of unequal elevation and pitch to be joined without the necessity of support columns and carrying beams. Further, a fan-like roof covering is provided by the gradually elevated tapered sheathing, resulting in an aesthetically appealing and structurally sound roof. 
     In accordance with an additional aspect of the present invention, an expansion roof includes a plurality of horizontally disposed rafter members disposed between end portions of a pair of roofs with tongue and groove sheathing members disposed across such rafter members. With such an arrangement, an aesthetically pleasing interior ceiling associated with the roof is provided which eliminates interior finishing materials, such as plaster or dry wall for the ceiling thereby further reducing the cost of building and also eliminates costly interior support structures. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the concepts of this invention, reference is now made to the following description taken together in conjunction with the accompanying drawings, in which: 
     FIG. 1 is an isometric view of a building having a plurality of roofs including a roof constructed in accordance with the present invention; 
     FIG. 1A is a diagrammatical plan view of the plurality of roofs shown in FIG. 1; 
     FIG. 2 is an isometric view of a portion of the framing for the roof constructed in accordance with the invention shown in FIGS. 1, 1A; 
     FIG. 2A is a cross-sectional view of member 32 taken along line 2A--2A of FIG. 2; 
     FIG. 3 is an elevational view of the framing of the roof structure useful for determining the length of framing members of the roof; 
     FIG. 4A is a side view of a plank of wood with plumb lines drawn thereon, used in fabricating expansion rafters for the roof of FIG. 1; 
     FIGS. 4B-4C are a series of isometric views showing additional steps in construction of the rafters used in a portion of the framing for the roof shown in FIG. 1; 
     FIGS. 4D-4E are end views of the rafters showing bevel angles used to provide a tapered, beveled surface; 
     FIG. 4F is an isometric view of an expansion rafter 34a having a tapered, beveled surface, constructed in accordance with FIGS. 4A-4E; 
     FIG. 5 is a plan view of a portion of the roof shown in FIG. 1 with sheathing disposed across the expansion rafters; and 
     FIG. 6 is an elevational view of a portion of the roof shown in FIG. 1 and FIG. 5. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to FIGS. 1 and 1A, a building 10 is shown to include a framing for a modified gable roof 20 and a hip roof 40 here joined together by framing for an expansion roof 30 disposed between said gable roof 20 and hip roof 40, as shown. The building further includes conventionally framed exterior walls 12a, 12b, as shown. Disposed and fastened to upper edge surfaces of such exterior walls are horizontally disposed flat members 14a-14h commonly referred to as top plates. 
     Modified gable roof (gable roof) 20 here includes a center horizontally disposed member 22, generally referred to as a ridge board, supported on opposing facial surfaces thereof, by a plurality of spaced members 26a-26f and 27a-27f extending between the ridge board 22 and plates 14c, 14e, as shown. The plurality of spaced members or, as generally referred to as common rafters 26a-26f, 27a-27f, are thus extended from the ridge board 22 to the plates 14c, 14d, respectively, at a 90° angle with respect to the ridge board 22 and respective ones of such plates 14c, 14e. Modified gable roof 20 here includes a pair of divergently spaced members 24a, 24b commonly referred to as hip rafters. Hip rafters 24a, 24b here are connected together in a conventional manner at an end portion 22&#39; of ridge board 22 and extend divergently outward to end portions 14c&#39;, 14e&#39; of plates 14 c, 14e, respectively. Hip rafters 24a, 24b are connected between corner portions 15c, 15e of plates 14c, 14e and the ridge board 22 at an angle of 45° , as is known in the art. Modified gable roof 20 further includes hip support members 23a, 23b and 25a, 25b commonly referred to as hip jack rafters, here extending between spaced portions along hip rafters 24a, 24b to spaced portions of plates 14a, 14b, respectively, as shown. 
     Hip roof 40 here includes a second central horizontal member or ridge board 42 here supported by a plurality of spaced common rafters 46a-46f, 47d-47f, as shown. Common rafters 46a-46f here extend between ridge board 42 and plate 14a, and the common rafters 47d-47f here extend between ridge board 42 and the plate 14f. Hip roof 40 further includes a plurality of divergently spaced members or hip rafters, here 44a-44e. In particular, hip rafter 44a here extends between an end portion 42&#39; of ridge board 42 and an end portion 15b of plate 14, and hip rafter 44b here extends between an end portion 42&#39; and a first end 15f of plate 14f. Ridge board 42 is also supported by a pair of common rafters 48a, 48b disposed between hip rafters 44e, 44a and 44d, 44c. Common rafters 48a, 48b bisect plates 14b and 14g, respectively. Hip rafters 44a-44e here are further supported by a plurality of hip jack rafters 43a-43n. Ridge board 42 is also supported by members 49a, 49b commonly referred to as valley jack rafters, as shown. A horizontal member 41 commonly referred to as a collar tie is connected between plates 14a and 14f, as shown. 
     It is to be noted here that modified gable roof 20 is at a first elevation e 1  from the ground and has a predetermined ratio (H 1  /R 1 ) of roof run (R 1 ) to roof rise (H 1 ), said ratio or pitch determining the slope of the roof. It is also to be noted that gable roof 20 would also include conventional laid horizontal sheathing (here not shown). The pitch of modified gable roof 20 is here five inches rise per twelve inches run. Similarly, hip roof 40 is at a second, here lower, elevation e 2  from the ground and has a predetermined pitch T 2  /h 2  here of five inches rise per twelve inches run. It is here noted that hip roof 40 would also include conventional laid horizontal sheathing (not shown). The difference in elevation between modified gable roof 20 and hip roof 40 is here 2 feet. Said elevational difference is represented by verticle members 17a, 17b of the exterior wall 12b. 
     Referring now also to FIGS. 2 and 2A, a frame for a portion 30&#39; of the expansion roof 30 shown in FIGS. 1 and 1A is shown to include a first horizontal center member 32 fabricated in a manner to be described, joined in a conventional manner at end portions 32a, 32b thereof to central horizontal members 42 and 22 of roofs 40 and 20, respectively. Horizontal center member here has a pair of longitudinally or bevel surface portions 32&#39;,32&#34; (FIG. 2A) extended from end 32a to end 32b and fabricated in a manner to be described. End portions 32a, 32b here have double end cuts at a selected angle or compound angle in accordance with the respective pitch of the center member 32. The ends 32a, 32b and the pair of tapered, beveled surfaces 32&#39;, 32&#34; are fabricated in a manner to be described in conjunction with FIGS. 4A-4F. The expansion roof 30 is shown to further include a plurality of expansion rafters 34a, 34b and 36a, 36b, each having a tapered, beveled surface portion 35a, 35b, 37a, 37b providing a curved centerline 35a, 35b, 37a, 37b to be described in conjunction with FIGS. 4A-4F. The expansion rafters 34a, 36a here extend between hip rafter 24a and hip rafter 44a and said expansion rafters 34b, 36b here extending between hip rafter 24b and hip rafter 44b. A horizontal member 39 commonly referred to as a collar tie is here connected between plate 14c and plate 14e, as shown. The collar tie is here used to aid in support of exterior wall 12b and the opposite wall (not numbered) disposed under plate 14e. In certain embodiments of the building, the collar tie may be omitted such as when plate 14c is not colinear with plate 14b, providing a protruding portion (not shown) of exterior wall 12b. At this juncture, it should be noted that here with respect to hip roof 40, members 44b, 44c are hip rafters, whereas with respect to the expansion roof 30, said members 44b, 44c are valley rafters, that is, said members 44b, 44c are provided at the intersection of a pair of roofs providing a depressed region or valley at the intersection of such roofs. 
     Referring again to FIGS. 1 and 1A, a generally known technique for determining a theoretical length l t  of hip rafters 24a, 24b, 44a and 44b will be described. The theoretical length l t  of a hip rafter such as hip rafter 44a, for example, is determined from the the run and rise of the hip rafter, as is known in the art, where the run is represented as the hypothenuse AC of an isosceles right triangle ABC having a first leg equal to the run of a common rafter 48a, and a second leg equal to one half the length of plate 14b which is also equal to the run of common rafter 48a. Since a unit run (u t48a ) of common rafter 48a is 12&#34;, a theoretical unit run u tr44a  of the hip rafter 44a is given as: u tr44a  =((u t48a ) 2  +(u t48a ) 2 ) 1/2  or u tr44a  =(12&#34; 2  +12&#34; 2 ) 1/2  ==(12&#34; 2  +12&#34; 2 ) 1/2  =17&#34;. Having determined the unit run of hip rafter 44a for example to be 17&#34; per foot run of common rafter, the theoretical length l t  can be determined for any pitch roof by use of a table entitled &#34;length of hip rafter per foot run,&#34; generally found on a framing square. The number in such table underneath the pitch of hip rafter 44a provides the unit length of hip rafter 44a per unit run of common rafter 48a. The number is then multiplied by the total theoretical run of the common rafter 48a to obtain the theoretical length l t44a  of such hip rafter 44a. 
     Having found the theoretical lengths, l t24a ,l t24b ,l t44a , l t44b  of the hip rafters, the actual lengths l a  are determined by subtracting therefrom a length equal to the allowance for the thickness of the ridge pole as is known in the art or as commonly referred to as &#34;the shortening allowance.&#34; Thus, for hip rafters disposed against ridge boards 26, 46, the ridge allowance is equal to one-half the 45° thickness of such ridge board 22 or 42 or one half of the length of a line drawn across the edge portion of such ridge board at a 45° angle. Thus, the shortening allowance for the ridge board l s  is used in combination with the theoretical length of the hip rafters to obtain l a  the actual length as:l t  -l s  =l a . 
     Referring now to FIGS. 3 and 4A-4E, steps in the construction of the expansion rafters 34a, 34b and 36a, 36b and central horizontal member 32 having tapered, beveled surfaces will be described. 
     Referring first to FIG. 3, the determination of actual lengths l a  of ridge board 32 and each one of the expansion rafters (rafter members) 34a, 34b, 36a, 36b will be described. 
     The actual length l a  of rafter members 34a, 34b, 36a, 36b and of ridge board 32 is equal to a calculated theoretical length l t  minus a length l s  determined by the angular thickness of the members to which expansion rafters 34a, 34b, 36a, 36b are attached, or the shortening allowance, as described above. The theoretical length of such expansion rafters 34a, 34b, 36a, 36b and 32 is here determined by the pitch of each one of such members. 
     The simplest case is where roofs 20&#39; (shown in phantom) and 40 are provided having equal elevations and pitches. In this case, a ridge board 132 (shown in phantom) is at right angles to common rafters 48a and 126a (shown in phantom) and, thus, the length of such ridge board 132 is equal to the combined length of portions 14b&#39; and 114c&#39; of plate 14b and a plate 114c (shown in phantom). It is to be noted that the respective run of common rafters 45a, 24a equals the respective lengths of portions 14b&#39;, 114c&#39; of plates 14b, 114c (shown in phantom), as is known in the art. 
     For the case where the ridge board 32 is adjoining ridge boards of roofs 20, 40 of equal pitch and different elevation as shown in FIG. 1, FIG. 1A, the length of such ridge board is determined from the difference in elevation and the run of the ridge board 32. As shown in FIG. 3, the theoretical length l t32  of such ridge board 32 is represented by the hypothenuse AC of a right triangle ABC, where side BC is representative of the difference in elevation of the roofs 20, 40 here the height of members 17a, 17b and side AB is the length of the ridge board 132 as previously determined above to be equal to twice the run of one of common rafters 24a, 48a. Thus, the length of such expansion ridge board 32 is given by: 
     
         l.sub.t32 =((l.sub.t132).sup.2 +(h.sub.17a).sup.2)1/2 
    
     using Phythagorean&#39;s Theorem. 
     In a similar manner, by using the runs of jack rafters 23a, 23b, 25a, 25b and 43a, 43b, 45a, 45b, the respective lengths l 34a , l 34b , l 36a , l 36b  of expansion rafters 34a, 34b,  36a, 36b may be determined from: 
     
         l.sub.t34a =l.sub.t34b =((14b&#34;&#39;+14c&#34;&#39;).sup.2 +(h.sub.17a).sup.2).sup.1/2, and 
    
     
         l.sub.t36b =lt.sub.36b =((14b&#34;+14c&#34;).sup.2 +(h.sub.17a).sup.2).sup.1/2 as shown in FIG. 3B. 
    
     Referring now to FIGS. 4A-4E, fabrication of a selected one of the curvatured, tapered expansion rafters 34a, 34b, 36a, 36b, here expansion rafter 34a will be described. It is to be noted that expansion rafters 34a, 34b and 36a, 36bare fabricated in pairs with one of such rafters 34a, 36a being the complement of the other remaining one 34b, 36b as is generally known for hip rafters. 
     Referring first to FIG. 4A, a plank 50 here of wood 4&#34; by 8&#34;nominally dimensional comprised of douglas fir has marked-off on face portion 51a thereof, a pair of lines P t1 , P t2  representative plumb lines which determine the cut of such member, here 34a, to correspond to the pitch of such member 34a. Lines are drawn at each end of the plank 50 representative of the theoretical length of the rafters 34a. The determined plumb lines are then drawn across the face 51a, of plank 50 at the end portion of the plank corresponding to the theoretical length of the rafter, as shown. Thus, on the face 51a, at end portion 50a of plank 50 is provided a first plumb line P tl  representative of the first plumb cut. End portion 50a of the rafter 32a shown in FIG. 1 rests against or on and is fastened to the lower hip rafter 42a (FIG. 1). Similarly, end portion 50b is provided with a second plumb line P tb  representative of a second plumb cut, and thus end portion 50b is the portion of the expansion rafter, here 34a (FIG. 1) which rests against the hip rafter 24a of the higher elevation roof 40. Thus, by using a framing square 60 as is known in the art, lines P t1 , P t2  representative of plumb cuts are drawn along the face 51a of plank 50 along a tongue 60a portion or shorter portion of the framing square which is positioned to denote the unit rise of the rafter 34a while a body portion 60b or longer portion of the framing square is positioned to denote the unit run of the rafter 34a. 
     For example, as shown in FIG. 3, expansion rafter 34a is denoted as the hypothenuse AC of a right triangle ABC, where side 34a&#39; (AB) is the length of a rafter 134a previously determined to be equal to the sum of the lengths 14b&#34;&#39;, 14c&#34;&#39;and CB is the elevational difference in the roofs 20, 40 denoted by verticle member 17a, 17b. The slope of such member 34a is determined as rise/run. Thus, here 14b&#34; and 14c&#34;&#39; are each 3 feet or pairs of adjacent jack rafters 23a, 23b and 43a, 43b are spaced apart by three feet. The slope is thus 2 ft./6 ft., or put another way there is 24&#34; of rise per six feet of run or 4&#34; rise per foot of run for expansion rafter 34a. Similarly, expansion rafter 36a has a rise of 2 feet in a run of 12 feet (combined lengths of 14b&#34; and 14c&#34;), thus, the slope is 2 ft./12 ft. or 24&#34; of rise per 12 feet of run or 2&#34; rise per foot run. Center ridge member 32 similarly has 24&#34; of rise per 18 feet of run or 1.3&#34; rise per foot of run. Thus, here the body portion 60b at 12&#34; mark of the framing square 60 is aligned with the plank 50 representative of the unit run of expansion rafter 34a and the tongue portion 60a at the 4&#34; mark of the framing square is aligned with the plank 50 representative of the unit rise of the roof. The plumb line P t1  is drawn at end portion 50a by drawing a line from a point on the plank representative of the theoretical length of the rafter as described above, along the tongue portion of the framing square, as shown. 
     In a similar manner, the plumb line P t2  is drawn at end portion 50b by moving the framing square 60 to end portion 50b such that the tongue portion 60a is aligned with the end portion 50b, and by drawing a line along the tongue portion of the framing square, as shown in FIG. 4A. 
     Referring now to FIG. 4B, having drawn lines P t1 , P t2  representative of the theoretical plumb cuts, plumb lines P a1 , P a2  representative of actual plumb cuts through the actual length of the expansion rafter 34a (FIG. 1), (i.e. the theoretical length minus the correction for the thickness of hip rafters 24a, 24b for example, as previously described) are provided. Lines S 1 , S 2  are drawn on an edge portion 52a of plank 50, here representing side cuts of the expansion rafter 34a or that angle at which the expansion rafter 34a joins the hip rafters 24a, 44a, for example, as shown in FIG. 1. In general, as for hip and valley rafters as is known in the art, the side angle cut is substantially equal to 45° for each one of the expansion rafters. However, as is also known in the art, when joining roofs at different elevations, hip rafter side cuts must be corrected in accordance with the difference in elevation or pitch of the member. Thus, the side cuts are substantially 45°. Here the side cuts are at 44°, 43.5° and 42° for ridge board 32 and expansion rafters 36a and 34a, respectively. 
     The location for side cut lines are determined as follows: As shown in FIG. 4B, a centerline C L  is shown drawn on edge 52a of plank 50. Plumb lines P t1  and P t2  on face portions 51a of plank 50 are projected across the edge surface 52a to intersect the centerline at a right angle. Actual plumb lines P a1 , P a2  are drawn parallel to the theoretical plumb lines P t1 , P t2 , through points on the plank 50 determined by the actual rafter length (l t  -l sa  =l a  side cut lines S 1 , S 2  are then drawn from the actual plumb lines P a1 , P a2  at the predetermined angle, here of 42° through the intersection of the extension of the theoretical plumb lines P t1 , P t2  and centerline C L  at each end portion 50a, 50b. A cut is then made with a suitable means, such as a saw through the plank 50 along the side cut lines S 1  , S 2  and along the plumb lines P a1 , P a2  to provide end portions 50a&#39;, 50b&#39;, as shown in FIG. 4C. 
     Referring now to FIGS. 4C-4F, a tapered, beveled surface is provided to the plank 50 of FIG. 4C to provide the expansion rafter 34a having a tapered, beveled surface 35a (FIG. 4F) used in accordance with the roof 30 shown in FIG. 1. 
     As shown in FIG. 4C, and in more detail in FIGS. 4D, 4E, selected bevel angles φ 1  (FIG. 3D) and φ 2  (FIG. 3E) are marked-off on each end portion 50a, 50b of the plank 50. These selected bevel angles φ 1 , φ 2  provided on end portions 50a, 50b are determined as follows: The bevel angle φ 1  at end portions 50a of plank 50 is determined by the angular sum of the slope of hip rafter 44a and the slope of the expansion rafter 34a. That is, the slope in degrees of hip rafter 44a is the ratio of unit run to unit rise of such hip rafter 44a, or θ 44a  =tan -1  (u h44a  /u r44a ). The slope in degrees of expansion rafter 34a is determined by the tangent of the ratio of unit rise to unit run or the difference in elevation between each of such roofs 20, 40 in relation to the run or length of such rafter 34a, as shown in FIG. 2. Thus, the bevel angle φ 1  for end portion 50a of plank 50 is given as: 
     
         φ.sub.1 =θ.sub.44a +θ.sub.34a or φ.sub.1 =tan.sup.-1 (u.sub.h44a /u.sub.r44a)+tan.sup.-1 (u.sub.h34a /u.sub.r34a). 
    
     Similarly, the slope in degrees of hip rafter 24a is determined as the θ 24a  =(tan -1  (u h24a  /u r24a ). The bevel angle φ 2  at the end portion 50b of plank 50 is determined by the difference of the angular slope of hip rafter 24a and the angular slope of expansion rafter 34a. Thus, the bevel angle φ 2  for end portion 50b is given as: 
     
         φ.sub.2 =φ.sub.24a -φ.sub.34a or φ.sub.2 =tan.sup.-1 (u.sub.h24a /u.sub.r24a)-tan.sup.-1 (u.sub.h34a /u.sub.r34a). 
    
     As an example, bevel angles φ 1  and φ 2  are determined as follows: recalling that roofs 20 and 40 each have a pitch of 5&#34;/12&#34; or slope of 22.5° for hip rafters 24a, 44a and expansion rafter 34a has a pitch of 4&#34;/12&#34; as determined above, or a slope of 18.5° , φ 1  and φ 2  are given as φ 1  =22.5° +18.5° =41°, and φ 2  =22.5°-18.5°=4° . The bevel angles φ 1 , φ 2  are transferred to the plank 50 with respect to an unbeveled edge 53a and lines B 1 , B 2  are drawn along ends 50a&#39;, 50b&#39; to the surface portion 51a of the plank 50 as shown in FIGS. 4D, 4E. A tapering line 54 is then drawn along surface portion 51a interconnecting such markings, indicating the taper of the expansion rafter. 
     The tapered, beveled surface 35a and a curvatured centerline 35b are then provided to plank 50 by planing the surface of the plank along the above-mentioned tapering line 54, from the unbeveled edge 53a, until the plane runs flat along unbeveled edge 53a and the tapering line 54 providing the expansion rafter 34a having the tapered, beveled surface 35a and curved centerline 35b, as shown in FIG. 4F. Each one of such remaining rafter members 34b, 36a, 36b and ridge board 32 are fabricated in a similar manner. Each pair of such members, namely, 34a, 34b and 36a, 36b have different plumb angles determined in accordance with the respective pair of such members. Further, each member of such pairs are fabricated in complement as generally done for hip rafters, as is known in the art. 
     Center member 32 is fabricated in a similar fashion as rafter members 34a, 34b, 36a, 36b, however, a pair of bevel taper surfaces are provided on center member 32. A pair of tapering lines are drawn on opposing facial surfaces (not shown) of center member 32 and such member is planed along each one of the tapering lines, with respect to a centerline (not shown) drawn down the center of the plank, providing the pair of beveled surfaces 32&#39;, 32&#34; shown in FIG. 2A. 
     Referring now to FIGS. 5 and 6, a preferred covering for the expansion roof 30 is shown to include a plurality of selectively tapered sheathing members 60a-60x and 60a&#39;-60x&#39;, disposed across the expansion rafters 34a, 34b, 36a, 36b, as shown. It is also to be noted that the sheathing is here tongue and grooved after cutting thereof, to provide an intimate fit between each of such members. However, other types of sheathing may be used including &#34;ship lap&#34; style and squared edged sheathing, as is known in the art. The tapered tongue and groove members 60a-60x and 60a&#39;-60x&#39; are fabricated as follows: each one of such members 60a-60x, 60a&#39;-60x&#39; have a first end portion having a width W 60  given as W 60  =l a32  /n where l a32  is the actual length of the expansion ridgeboard 32 and n is the member of sheathing members, here shown as 24. Each one of such members 60a-60x and 60a&#39;-60x&#39; have a bottom width given as 90°-221/2°/24=671/2/24=23/4°. Since the roof 30 is bounded by hip rafters such as 44b, 24a which have equal lengths and intersect at a right angle, 1° of pitch is equal to 1&#34; of bottom width. Thus, here stock planks 12&#34; wide are ripped to provide pairs of such sheathing elements 60 and 60&#39;, which may be provided on opposite surfaces of the roof 30. The cut planks may at this point be tongue and groove, and are then fitted into place by scribing and cutting the ends to fit in place, as is known in the art. 
     It is here to be noted that, as shown in FIG. 6, tapered sheathing members are laid across the expansion rafters 34a, 34b, 36a, 36b and ridge board 32, the pitch of sheathing members will gradually increase upward, following the tapered, curvatured surface of the expansion rafters 34a, 34b, 36a, 36b providing a fan-like appearance to the roof 30 when covered with such sheathing. 
     It is to be noted that the expansion roof may be fabricated by using expansion rafters not having a tapered, beveled surface. However, it shoud also be noted that when sheathing members are laid across such expansion rafters, the sheathing will not adequately follow the pitch of the roof leaving large voids between the sheathing members and portions of the expansion rafter. Thus, the preferred embodiment of the invention uses expansion rafters 34a, 34b, 36a, 36b having a tapered, beveled surface. 
     It is also to be noted that the expansion roof 30 may be fabricated with expansion rafters, provided with a beveled edge instead of the tapered, beveled edge providing the curvatured centerline described above. However, as described above, when roof sheathing is laid across these expansion rafters, the sheathing again will not adequately follow the pitch of the rafters and thus voids will exist between the sheathing and expansion rafter members. 
     However, for the situation where the adjoining roof 20 is at the same elevation and same pitch, then the slope of the horizontal or expansion rafter members will be equal to zero and thus the bevel angles φ 1 , φ 2  provided at end portions of the expansion rafters will be equal and thus a straight bevel may be cut along the selected surface of the expansion rafter, and such rafter will have a beveled edge without the curvatured centerline. 
     Further, it should also be noted that the expansion roof need not adjoin other roofs. That is, in certain applications, a suitable covering may be provided solely with a properly supported expansion roof. 
     Having described preferred embodiments of the invention, it will now be apparent to one of skill in the art that other embodiments incorporating its concept may be used. It is felt, therefore, that this invention should not be restricted to the disclosed embodiments, but rather should be limited only by the spirit and scope of the appended claims.