故宫古建筑斗拱中的科学

周 乾

作为我国优秀传统建筑文化的代表，故宫古建筑有着诸多的吸引国内外游客的魅力，而其中的典型特色之一，就是斗拱。斗拱是我国特有的古建筑组成构件，是位于柱顶之上、屋檐之下，由斗形、弓形的木构件在纵横方向搭扣连接，而后在竖向又层层叠加起来，形成的一道道组合，外形犹如撑开的伞状，见图1。

图1 柱顶之上的斗拱

故宫古建筑斗拱的主要构件包括坐斗、拱、翘等（图2）。这些构件的成形与我国古建筑演变密切相关。早期的宫殿建筑中，往往采用斜撑的木柱来支撑宽大的屋檐，斜撑分别设于屋檐的前后方。而为了避免落地的斜撑受雨水侵蚀，其下支点便离开了地面，称为短斜撑，并随着审美需求逐渐被弯曲的木料替代，形成了今天斗拱的横向重要构件——翘。同时，为了增强柱顶部位支撑屋檐的强度，柱顶之上又增加了斗形木块，形成了坐斗。不仅如此，木块上方沿着屋檐方向叠加长方形的垫木，这些长方形的垫木因审美需要逐渐变成弓形，形成了今天斗拱纵向的重要构件——拱。故宫古建筑斗拱不仅造型美观，更包含了丰富的古代力学智慧。

图2 斗拱的主要构件名称

斗拱的力学智慧精华在于它的抗震性能。笔者曾开展了故宫太和殿斗拱抗震性能的试验研究。试验显示：无论是水平向还是竖向的地震波，都不会造成斗拱破坏。发生水平地震时，斗拱的各个构件之间互相摩擦、挤压，并产生往复运动，犹如一个运动的机构体系。从能量守恒角度讲，地震波的能量传到斗拱位置时，主要分成了2个部分的能量：斗拱的内能及斗拱的动能，斗拱内能即自身产生开裂破坏的根本原因，内能越大，斗拱破坏越严重。然而斗拱能量的另一个组成部分即动能占的比例远大于自身的内能，其原因在于每个斗拱由上百个小构件组成，它们犹如机器的零件一样，在地震作用是不断产生各种运动，耗散了大量的地震能量，从而使得斗拱内能的比例很小，因而斗拱在地震作用下几乎不会产生破坏。事实上，大量的古建震害勘查结果表明，斗拱在地震作用下一般保存完好。

不仅如此，水平地震作用下，斗拱还能产生自动恢复功能，犹如不倒翁一样，其原因在于斗拱特殊的构造特征。这种构造特征使得：一方面斗拱的重心位于斗拱的下方，斗拱犹如一个矮胖的人，在水平地震力（推拉力）作用下尽管产生摇摆，但是不易倾覆；另一方面坐斗的截面尺寸宽大，这无疑增大了斗拱与其底部的接触面，斗拱在水平地震作用下产生摇摆时，分别绕着坐斗两侧的支点进行摇摆（图3）。而在斗拱摇摆过程中，其上部屋顶的重量迫使斗拱不断地复位，因而斗拱像不倒翁一样，不断地来回摆动。地震波结束后，斗拱又恢复到了初始位置，本身并未受到损害。

图3  水平地震作用下斗拱摇摆示意图

笔者基于科学分析，发现故宫古建筑斗拱还能够抵抗竖向地震作用。其原因在于，斗拱由木材制成，木材弹性模量很小，很容易产生变形并迅速恢复原状，犹如弹簧一样。斗拱在竖向由一层层构件叠加起来，就像一层层弹簧连起来一样（图4）。斗拱层数越多，弹簧的柔性越大。发生竖向地震时（实际上地震波在水平、竖向同时产生），尽管竖向的地震力很大，但是斗拱整体像弹簧一样反复做压缩→复原运动，可以不断地削弱地震力，有着“以柔克刚”的特性。从能量守恒角度讲，竖向地震波的能量传到斗拱位置时，分解成为斗拱的动能、势能、内能，而其中前二者的比例非常大，使得斗拱的内能的比例很小，因而斗拱不会因为受到的内力过大而产生破坏。实际上，斗拱的这种弹簧特性的抵抗地震的方法，从科学的角度可称为“隔震”。

图4  太和殿一层斗拱外立面侧视

综上可知，故宫古建筑斗拱精巧的构造及优秀的抗震性能，汇聚了我国古代工匠卓越的建筑智慧和丰富的工程经验，亦为中华优秀传统文化的重要组成部分。

（《知识就是力量》2024年第2期刊载，有修改）

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.1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media screen and (min-width:1024px) and (prefers-color-scheme:dark){body:not(.pages_skin_pc) .wx-root:not([data-weui-theme=light]),body:not(.pages_skin_pc) body:not([data-weui-theme=light]){--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media screen and (min-width:1024px) and (prefers-color-scheme:dark){body:not(.pages_skin_pc) .wx-root:not([data-weui-theme=light]),body:not(.pages_skin_pc) body:not([data-weui-theme=light]){--appmsgExtra-BG: #121212}}@media(prefers-color-scheme:dark){body:not([data-weui-theme=light]).my_comment_empty_data{background-color:#111}}body,.wx-root{--weui-BG-6: rgba(0, 0, 0, .05);--weui-ACTIVE-MASK: rgba(0, 0, 0, .05)}body,.wx-root{--weui-REDORANGE: #ff6146;--weui-BG-0: #ededed;--weui-BG-1: #f7f7f7;--weui-BG-2: #fff;--weui-BG-3: #f7f7f7;--weui-BG-4: #4c4c4c;--weui-BG-5: #fff;--weui-FG-0: rgba(0, 0, 0, .9);--weui-FG-HALF: rgba(0, 0, 0, .9);--weui-FG-1: rgba(0, 0, 0, .55);--weui-FG-2: rgba(0, 0, 0, .3);--weui-FG-3: rgba(0, 0, 0, .1);--weui-FG-4: rgba(0, 0, 0, .15);--weui-FG-5: rgba(0, 0, 0, .05);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #fa9d3b;--weui-YELLOW: #ffc300;--weui-GREEN: #91d300;--weui-LIGHTGREEN: #95ec69;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1485ee;--weui-PURPLE: #6467f0;--weui-WHITE: #fff;--weui-LINK: #576b95;--weui-TEXTGREEN: #06ae56;--weui-FG: #000;--weui-BG: #fff;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: #fa9d3b;--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: #06ae56;--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: #10aeff;--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(0, 0, 0, .5);--weui-TAG-BACKGROUND-BLACK: rgba(0, 0, 0, .05)}body,.wx-root{--weui-BG-0: #ededed;--weui-BG-1: #f7f7f7;--weui-BG-2: #fff;--weui-BG-3: #f7f7f7;--weui-BG-4: #4c4c4c;--weui-BG-5: #fff;--weui-FG-0: rgba(0, 0, 0, .9);--weui-FG-HALF: rgba(0, 0, 0, .9);--weui-FG-1: rgba(0, 0, 0, .55);--weui-FG-2: rgba(0, 0, 0, .3);--weui-FG-3: rgba(0, 0, 0, .1);--weui-FG-4: rgba(0, 0, 0, .15);--weui-FG-5: rgba(0, 0, 0, .05);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #fa9d3b;--weui-YELLOW: #ffc300;--weui-GREEN: #91d300;--weui-LIGHTGREEN: #95ec69;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1485ee;--weui-PURPLE: #6467f0;--weui-WHITE: #fff;--weui-LINK: #576b95;--weui-TEXTGREEN: #06ae56;--weui-FG: #000;--weui-BG: #fff;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: #fa9d3b;--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: #06ae56;--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: #10aeff;--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(0, 0, 0, .5);--weui-TAG-BACKGROUND-BLACK: rgba(0, 0, 0, .05)}.wx-root,body{--weui-BTN-ACTIVE-MASK: rgba(0, 0, 0, .1)}.wx-root,body{--weui-BTN-DEFAULT-ACTIVE-BG: #e6e6e6}.wx-root,body{--weui-DIALOG-LINE-COLOR: rgba(0, 0, 0, .1)}.wx-root,body{--weui-BG-COLOR-ACTIVE: #ececec}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BTN-ACTIVE-MASK: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BTN-DEFAULT-ACTIVE-BG: rgba(255, 255, 255, .126)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-DIALOG-LINE-COLOR: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--APPMSGCARD-BG: #1E1E1E}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--APPMSGCARD-LINE-BG: rgba(255, 255, 255, .07)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-COLOR-ACTIVE: #373737}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-6: rgba(255, 255, 255, .1);--weui-ACTIVE-MASK: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-REDORANGE: #ff6146;--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--discussInput-BG: rgba(255, 255, 255, .03)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--nickName-FG: #959595}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--appmsgExtra-BG: #121212}}@media(prefers-color-scheme:dark){body:not([data-weui-theme=light]) .rich_media_content img:not(.wx_img_placeholder){filter:brightness(.8)}}*{margin:0;padding:0}.rich_media_content *{max-width:100%!important;box-sizing:border-box!important;-webkit-box-sizing:border-box!important;word-wrap:break-word!important}

div.autoTypeSetting24psection > p,div.autoTypeSetting24psection > section{margin-bottom: 24px;}