《第四节：压杆的稳定计算（一）》单元教学设计

1、工程力学单元教学设计水工建筑物教学文本压杆的稳定计算（一）单元教学设计1. 教案计划表单元名称第十章 压杆稳定学时1项目名称第四节 压杆的稳定计算（一）教学地点多媒体教室学生角色设计辅助人员教学目标知识目标技能目标态度目标（1）了解压杆稳定条件；（2）理解折减系数法和安全系数法；（1）能够说明压杆稳定的条件；（2）能够熟练掌握安全系数法和折减系数法；并能够准确查找和确定安全系数和折减系数；（1）做好课前预习、课后复习；（2）能够按时上课，遵守课堂纪律，积极回答课堂问题，实现有效的互动和交流；（3）课下同学间能对疑难问题相互讨论，能认真完成老师布置的各项任务，按时上交作业。（4）注重提出、分析、

2、解决问题此逻辑思维能力的培养；（5）能勇于表达个人的观点和见解。能力训练任务及案例由许用应力的概念引出压杆稳定条件，并说明压杆稳定条件的折减系数法和安全系数。教学重点、难点重点：压杆稳定条件，折减系数法，安全系数法。难点：折减系数法。教学方法、手段案例法，讲练结合法，黑板、多媒体课件，动画。教学组织过程 （1）复习回顾：压杆临界应力的计算方法和许用应力的概念。（2）引入案例：压杆稳定的条件，说明折减系数法。（3）提出问题：压杆稳定的条件，折减系数法的原理。（4）教师辅导评价；教师进行全过程答疑，观察学生的完成的质量，根据逻辑的完整性进行评价。（5）最后总结：阐明在计算过程中出现的系列问题和注意

3、事项，进一步完善解决问题的方法。教学条件多媒体教学课件和配套设备，课程相关资料。作 业基础试题（填空题、简答题等）备 注2. 教学实施【步骤l】复习巩固和引入新课教学地点教师任务学生任务教学条件时间（分钟）多媒体教室学习任务引入与教师互动回答多媒体课件5【步骤2】课程介绍及知识讲授教学地点教师任务学生任务教学条件时间（分钟）多媒体教室讲解本章的几个知识点听课，获取有关知识和信息多媒体课件25教学内容及要求：1压杆稳定条件在工程中，为了保证压杆在轴向压力作用下不致失稳，必须使其横截面上的工作应力满足下述条件： （10-14）式中：为压杆的工作应力；为稳定容许应力；为稳定安全系数。在选择稳定安全系

4、数时，除应遵循确定强度安全系数的一般原则外，还应考虑加载偏心与压杆原本存在弯曲现象等不利因素。因此，稳定安全系数一般大于强度安全系数。其值可从有关设计规范中查得。对于金属结构中的压杆，稳定安全系数一般取1.83.0。2折减系数法为了计算上的方便，在工程实际中，常采用折减系数法进行稳定计算。将稳定容许应力值写成下列形式，则稳定条件为 或 式中：为强度计算时的容许压应力；为压杆轴力；A为压杆横截面的面积，截面的局部削弱对整体刚度的影响甚微，因而不考虑面积的局部削弱，但要对削弱处进行强度验算；是一个小于1的系数，称为稳定系数或折减系数。因为临界应力和稳定安全因数总是随柔度的改变而改变，故稳定系数与压

5、杆的柔度、所用材料、截面类型等有关，其值可从有关设计规范中查得。在钢结构设计规范（GB50017-2003）中，根据工程中常用构件的截面形式、尺寸和加工条件等因素，把截面归并为a、b、c、d四类，表10-2、表10-3仅列出了三类。表10-4、表10-5、表10-6给出了 钢对应a、b、c三类截面在不同柔度下的值。在木结构设计规范（GB5005-2003）中，按树种的强度等级分别给出的两组计算公式，如下所示：（1）树种强度等级为：TC15、TC17及TB20： （10-15）（2）树种强度等级为：TC11、TC13、TB11、TB13、TB15及TB17： （10-16）表10-2 轴心受压构

6、件的截面分类(板厚)截面形式对x轴对y轴 轧制a类a类 轧制，a类b类轧制，焊接，翼缘为焰切边焊接b类b类轧制轧制等边角钢轧制，焊接(板件宽厚比20)轧制或焊接b类b类焊接轧制截面和翼缘为焰切边的焊接截面b类b类格构式焊接，板件边缘焰切焊接，翼缘为轧制或剪切边b类c类焊接，板件边缘为轧制或剪切焊接，板件宽厚比20c类c类表10-3 心受压构件的截面分类(板厚)截面形式对x轴对y轴 轧制工字形或H形截面b类c类轧制工字形或H形截面c类d类焊接工字形截面翼缘为焰切边b类b类翼缘为轧制或剪切边c类d类焊接箱形截面板件宽厚比20b类b类板件宽厚比20c类c类表10-4 钢a类截面轴心受压构件稳定系数0

7、12345678901020304050607080901001101201301401501601701801902002102202302402501.0000.9950.9810.9630.9410.9160.8830.8390.7830.7140.6380.5630.4940.4340.3830.3390.3020.2700.2430.2200.1990.1820.1660.1530.1410.1301.0000.9940.9790.9610.9390.9130.8790.8340.7760.7060.6300.5550.4880.4290.3780.3350.2980.2670.24

8、10.2180.1980.1800.1650.1520.140-1.0000.9930.9770.9590.9370.9100.8750.8290.7700.6990.6220.5480.4810.4230.3730.3310.2950.2640.2380.2150.1960.1790.1640.1500.139-1.0000.9920.9760.9570.9340.9070.8710.8240.7630.6910.6150.5410.4750.4180.3690.3270.2920.2620.2360.2130.1940.1770.1620.1490.138-0.9990.9910.9740

9、.9550.9320.9040.8670.8180.7570.6840.6070.5340.4690.4120.3640.3230.2890.2590.2330.2110.1920.1750.1610.1480.136-0.9990.9890.9720.9520.9290.9000.8630.8130.7500.6760.6000.5270.4630.4070.3600.3200.2850.2560.2310.2090.1900.1740.1590.1470.135-0.9980.9880.9700.9500.9270.8970.8580.8070.7430.6680.5920.5200.45

10、70.4020.3560.3160.2820.2530.2290.2070.1890.1720.1580.1460.134-0.9980.9860.9680.9480.9240.8940.8540.8010.7360.6610.5850.5140.4510.3970.3510.3120.2790.2510.2260.2050.1870.1710.1570.1440.133-0.9970.9850.9660.9460.9210.8900.8490.7950.7280.6530.5770.5070.4450.3920.3470.3090.2760.2480.2240.2030.1850.1690.

11、1550.1430.132-0.9960.9830.9640.9440.9190.8860.8440.7890.7210.6450.5700.5000.4400.3870.3430.3050.2730.2460.2220.2010.1830.1680.1540.1420.131-表10-5 钢a类截面轴心受压构件稳定系数012345678901020304050607080901001101201301401501601701801902002102202302402501.0000.9920.9700.9360.8990.8560.8070.7510.6880.6210.5550.4930.

12、4370.3870.3450.3080.2760.2490.2250.2040.1860.1700.1560.1440.1330.1231.0000.9910.9670.9320.8950.8520.8020.7450.6810.6140.5490.4870.4320.3830.3410.3040.2730.2460.2230.2020.1840.1690.1550.1430.132-1.0000.9890.9630.9290.8910.8470.7970.7390.6750.6080.5420.4810.4260.3780.3370.3010.2700.2440.2200.2000.1830

13、.1670.1540.1420.131-0.9990.9870.9600.9250.8870.8420.7910.7320.6680.6010.5360.4750.4210.3740.3330.2980.2670.2410.2180.1980.1810.1660.1530.1410.130-0.9990.9850.9570.9220.8820.8380.7860.7260.6610.5940.5290.4700.4160.3700.3290.2950.2650.2390.2160.1970.1800.1650.1510.1400.129-0.9980.9830.9530.9180.8780.8

14、330.7800.7200.6550.5880.5230.4640.4110.3650.3260.2910.2620.2360.2140.1950.1780.1630.1500.1380.128-0.9970.9810.9500.9140.8740.8280.7740.7140.6480.5810.5170.4580.4060.3610.3220.2880.2590.2340.2120.1930.1760.1620.1490.1370.127-0.9960.9780.9460.9100.8700.8230.7690.7070.6410.5750.5110.4530.4020.3570.3180

15、.2850.2560.2320.2100.1910.1750.1600.1480.1360.126-0.9950.9760.9430.9060.8650.8180.7630.7010.6350.5680.5050.4470.3970.3530.3150.2820.2540.2290.2080.1900.1730.1590.1460.1350.125-0.9940.9730.9390.9030.8610.8130.7570.6940.6280.5610.4990.4420.3920.3490.3110.2790.2510.2270.2060.1880.1720.1580.1450.1340.12

16、4-表10-6 钢a类截面轴心受压构件稳定系数012345678901020304050607080901001101201301401501601701801902002102202302402501.0000.9920.9660.9020.8390.7750.7090.6430.5780.5170.4630.4190.3790.3420.3090.2800.2540.2300.2100.1920.1760.1620.1500.1380.1280.1191.0000.9900.9590.8960.8330.7680.7020.6360.5720.5110.4580.4150.3750.339

17、0.3060.2770.2510.2280.2080.1900.1750.1610.1480.1370.127-1.0000.9880.9530.8900.8260.7620.6950.6290.5660.5050.4540.4110.3710.3350.3030.2740.2490.2260.2060.1890.1730.1590.1470.1360.126-0.9990.9860.9470.8840.8200.7550.6890.6230.5590.5000.4490.4070.3670.3320.3000.2710.2460.2240.2050.1870.1720.1580.1460.1

18、350.125-0.9990.9830.9400.8770.8140.7480.6820.6160.5530.4940.4450.4030.3640.3280.2970.2690.2440.2220.2030.1860.1700.1570.1450.1340.124-0.9980.9810.9340.8710.8070.7420.6760.6100.5470.4880.4410.3990.3600.3250.2940.2660.2420.2200.2010.1840.1690.1560.1440.1330.124-0.9970.9780.9280.8650.8010.7350.6690.6040.5410.4830.4360.3950.3560.3220.2910.2640.2390.2180.1990.1280.1680.1540.1430.1320.123-0.9960.9760.9210.8580.7940.7290.6620.5970.5350.4770.4320.3910.3530.