两段变截面矩形悬挑梁挠度计算

两段变截面矩形悬挑梁挠度计算 唐大凡 摘要 本文采用虚功原理推导出两段变截面矩形悬臂梁(均质弹性材料)在各种荷载作用下的挠度计算公式，供 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 者参考。 关键词 变截面 悬臂梁 挠度计算 Deflection Calculation of Variable Cross-section Rectangle Vantilever Beam Tang Dafan (An Shan Metallurgical Engineering Design and Research Institute,the Ministry of Metallurgical Industry) ABSTRACT The formula for deflection calculation of variable cross-section rectangle vantilever beam is derived with virtual work theory.This paper has some reference value to engineering designer. KEYWORDS Variable cross-section Vantilever beam Defvlection calculation 一、问 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 的引出 意大利著名结构 工程 路基工程安全技术交底工程项目施工成本控制工程量增项单年度零星工程技术标正投影法基本原理 师Nervi P.L.在1932年为意大利佛罗伦萨体育场设计的看台顶棚采用了悬挑17m的悬挑梁，其外形与弯矩的二次抛物线图形相一致，是至今最著名的大跨度变截面悬挑梁之一。在结构设计中，由于建筑功能或建筑造型的需要结构工程师需设计大跨度的悬挑梁，诸如体育场主看台雨篷梁、电视塔及高层建筑顶部承托或悬挂旋转餐厅挑出部分的大梁。为了节省材料，减轻自重及增强美感大跨度挑梁常设计成变截面梁，但设计中必须严格控制其挠度。以往计算挠度多采用“分段总和法”近似求解，该法不仅计算过程繁冗、计算量大，而且计算过程极易出错。为此，作者采用虚功原理推导出两段变截面均质弹性材料悬挑梁在各种荷载作用下的挠度计算公式，所得值为弹性位移。设计中若为钢筋砼梁还须按《砼设计规范》进行刚度折减计算。 图1 计算简图 二、计算公式的推导 are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 两段变截面矩形悬挑梁如图1(a)所示，梁宽为b，其余结构尺寸及荷载见图。x轴的坐标原点取在固定端处。依据虚设单位力法先求实际荷载作用下的M(x)，再求虚设单位P 荷载(P=1)作用下的(x)。由于h/L值不很大，剪力对挠度的影响很小可忽略不计。以下分别导出梁在各种荷载作用下的自由端处(A点或A′点)挠度f。 1.均布荷载作用下的挠度f 1 实际荷载作用下M(x)为: P 虚设单位力(P=1)作用下(x)为: I(x)的计算如下: 则自由端处挠度f为: 1 (1) 式(1)中第1项积分值为: (2) are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 式中 式(1)中第2项积分值，当η?η时为 12 (3) 式中 当η=η时为: 12 (4) 2.集中荷载作用下的挠度f 2 实际荷载作用下M(x)为(见图2): P 虚设单位力作用下(x)为: I(x)的计算公式同前，则自由端处挠度f为: 2 are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 当L,b?L时 10 (5) 式(5)中第1项积分值为: (6) 式中a、a 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 达式同前。 12 式(5)第2项积分值为: 当η?η时 12 (7) 式中a、a表达式同前。 34 当η=η时 12 (8) 当0?b?L 01 (9) 式中a、a表达式同前。 12 3.在均布荷载和集中荷载共同作用下的挠度f的计算 3 分别按上述1、2求出自由端处的挠度f、Σf。将求得的f、Σf叠加即为所求挠度1212f: 3 are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female (10) 图2 图3 三、算例 ,2, 某变截面悬挑梁结构尺寸及荷载如图3所示、梁宽b=0.5m，试计算自由端处挠度f。 3 1.用本文推导公式计算 (1)在均布荷载作用下A点的f 1 由 L=7.1m,L=1.8m,L=8.9m,q=60kN/m,q=80kN/m,q=98kN/m,h=2.4m,b=0.5m,η=η=0.5计1212312算如下: are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 将上述值代入式(2)及(4)得f: 1 (2)在集中荷载作用下A点的f 2′ 将b=8.9m，P=170kN代入式(6)、(8)求其挠度f为: 02 ″ 将b=7.1m,P=70kN代入式(9)求其挠度f为: 02 are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 所以 (3)在均布及集中荷载共同作用下A点的总挠度f 3 2.用“分段总和法”计算 用“分段总和法”求其自由端处(A点)挠度f，其结果为:。计算3 中将变截面梁长7.1m分成9段，计算过程略。 通过对以上2种 方法 快递客服问题件处理详细方法山木方法pdf计算方法pdf华与华方法下载八字理论方法下载 的计算结果比较可见，用“分段总和法”近似求解变截面悬挑梁的挠度比本文给出的公式计算值偏小。仅就本例而言，偏小15.4%。 作者单位:冶金部鞍山冶金设计研究院 114002 参考文献 ,1, 包世华，结构力学教程，高等教育出版社 ,2, 陈元椿，深圳体育馆结构设计，建筑结构1991.4 are no special instructions below, in this report, the "I" mean green town in yingde city middle school, "we" means young qingtang town middle school in the Township of yingde city middle school teachers ' professional development study group. ) The actual condition and the specific situation of young teachers ' professional development for young teachers ' College ... (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female 34 70.83% beside the effective fill in passengers 48 from survey of data view, I school young teachers in the, female teachers 34 people, male teachers 14 people, high out 20 people; from by accounted for proportion view, female teachers accounted for than 70.83%, male teachers 29. 17%, ratio of female teachers account for 41.66 percent. Young teacher in our school can be seen in the serious imbalance in the sex ratio, obviously there with the current outlooks a greater relationship. This requires the attention of our Administrative Department of education high allocations in education issues. 2nd questions how old you are (a) [form] (A) (Young teachers of) basic information data analysis 1th problem you of gender () [single topics] option small meter proportion a,. male 14 29.17% b. female