jǔzhé 舉折

Note

Juzhe, literally “raise" and "bend, bow” (Kroll 2015, 226, 596), is a method of positioning the purlins in relation to each other in order to manipulate the slope and curvature of the roof. In premodern literature, the term juzhe only appears in the Yingzao fashi. According to this text, a building’s juzhe is determined through a process called ding ceyang 定側樣 (deciding the side appearance) or dian caojia 點草架 (designating the rough structural frame). During this process, the roof frame would be drawn on a wall plane at a scale of 1:10 (Li 2009, 5.9b). The drawing would then serve as a reference for determining the positions of the purlins during assembly. 4

Juzhe involves two steps, juwu 舉屋 and zhewu 折屋, which are to be performed in this order. Juwu (“raising the roof”) refers to positioning the ridge purlin in order to determine the total height of the roof (H) measured from the top of the eaves purlin to the top of ridge purlin. In the Yingzao fashi, the height of the ridge purlin (or the top of the roof slope) is stipulated according to the different rank of the buildings. The calculation of the height of the ridge purlin (H) is based on the depth of the building (D), measured by the horizontal distance between the front and rear eaves purlins or between the front and back columns if the building does not employ dougong. The height of the ridge purlin can be either 1/3 or 1/4 the building depth, depending on the rank of the building.

Zhewu (“bending” or “folding” the roof) occurs after juwu (“raising the roof”) has been completed and refers to determining the heights of all the purlins under the roof ridge in order to obtain a concave roof slope. Taking half of a building as an example, the distance between the ridge purlin and the eave purlin is divided based on the number of purlins necessary for the structure in question. After determining the height of the ridge purlin, the roof curvature is created by lowering the intermediary purlins from the slope created by casting a straight line from the eaves purlin to the ridge purlin (Figs. Step 2, 3). The top purlins (shangpingtuan 上平槫) are lowered from this slope by 1/10th the vertical distance between the eaves purlin and the roof ridge (h1). For each of the purlins beneath the shangpingtuan, the height is reduced by half of this distance based on a new slope, as shown in Figs. Step 4, 5, and 6. However, few buildings extant today were constructed exactly according to the description of juzhe in the Yingzao fashi. The final step (Fig. Step 7) would be to add a series of rafters between each purlin. These rafters form the substructure for the rooftile layer.

Among scholars of Chinese architectural history, there is no disagreement in the definition and practice of juzhe. However, concerning the description of the method of calculating zhewu, modern scholars usually summarize the concept as a mathematical formula with the height of the ridge purlin (H) as the only variable (Figs. Steps 3-6; Liang 1983, 493; Pan and He 2005, 51-53）The description in the Yingzao fashi may be closer to the craftsmen’s method of working, in which they obtained the distance of every purlin under the upper purlin by “folding in half” (zheban 折半) the distance of the purlin above it and repeating this method until all the eave purlins were positioned.5

舉折是確定各槫位置以獲得屋架折線的方法。在現有的古代文獻中，該術語僅出現於《營造法式》。按照《營造法式》中的描述，定舉折時應先以1:10的比例把屋架畫在平直的牆壁上（從而可確定各槫的位置），稱為“定側樣”或“點草架” (李 2009，5.9b)。 4

舉折包括“舉”（“舉屋之法”）和“折”（“折屋之法”）兩個部分，且先“舉”後“折”。“舉”是將一個物體抬起的意思。“舉屋之法”是確定脊槫位置，即確定脊槫抬起高度，也就是脊槫背到橑簷枋背高差的方法。在《營造法式》中，根據房屋等級的不同對脊槫抬起的高度做了規定。其基準是房屋的進深，即前後撩簷方（或不用斗栱時，前後簷柱）中心的距離。根據建築等級的不同，脊檩被举起的高度可以是進深的三分之一到四分之一。

“折”是曲折，彎的意思。“折屋之法”是確定脊槫以下各槫背的位置以獲得屋架折線的方法。每個槫的位置總是低於上一個槫背與橑簷方背中心連線與該槫縫相交應該的位置。《營造法式》對“折”的具體數值也做了規定。上平槫折的距離（即下降的高度）為舉高的十分之一（即以所得舉高，每尺折一寸），其後依次下降上一折的二分之一。但很少有完全符合《營造法式》“折屋之法”的現存實例。

現代建築史學者對舉折的涵義、做法沒有疑義。但在對“折屋”計算方法的表述中，採用了與《營造法式》不同的邏輯，將其總結為以脊檩抬起高度（H）為唯一變量的數學公式（梁 1983，493；潘和何 2005，51-53）。而《營造法式》的表述方式，很可能更接近工匠的工作方法，即以上平槫之折的數值折半再折半的方式獲得其下各槫的“折”的數值。5

Broad Match: building frame