【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」臺灣3.0版授權釋出】

Presentation on theme: "【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」臺灣3.0版授權釋出】"— Presentation transcript:

1 【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」臺灣3.0版授權釋出】
National Taiwan University Material Mechanics Chapter Five Stresses in beams 2014 Summer 國立臺灣大學土木工程學系 黃尹男 教授 【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」臺灣3.0版授權釋出】

2 Stresses in beams Class Introduction Class Pure bending & Non-uniform bending Class Curvature of a beam Class Longitudinal Strains in Beams Class Normal Stresses in Beams (Linearly Elastic Materials) Class Design of Beams for Bending Stresses Class Shear Stresses in Beams of Rectangular Cross Section Class Shear Stresses in Beams of Circular Cross Section Class Shear Stresses in the Webs of Beams with Flames Class 10. Built-Up Beams and Shear Flows

3 前情提要 [博升小語] 看懂推導過程是必要的…

4 Normal Stresses in Beams (Linearly Elastic Materials)
Class 5 Normal Stresses in Beams (Linearly Elastic Materials)

5 Normal Stresses in Beams (Linearly Elastic Materials)
記住這條公式， 後面推導會用 ~ [Assumption] Beam lengths are much greater to its lateral dimensions. (Otherwise, the derivations apply only to pure bending case.)

6 Normal Stresses in Beams (Linearly Elastic Materials)
[得證] The origin O of coordinates is located at the centriod of the cross-sectional area.

7 Normal Stresses in Beams (Linearly Elastic Materials)

8 Normal Stresses in Beams (Linearly Elastic Materials)
負號的意義是？ 我們做了哪些假設？

9 Normal Stresses in Beams (Linearly Elastic Materials)
Maximum Bending Stresses at a Cross Section

10 Normal Stresses in Beams (Linearly Elastic Materials)
Doubly Symmetric Cross Sections S: Section Modulus 斷面模數 [博升小語] Hey！先別急著笑這個推導怎麼這麼無聊 等你們出社會接觸實務就會發現其實大家都是在查表~

11 Normal Stresses in Beams (Linearly Elastic Materials)
常用的 I值 & S值 Normal Stresses in Beams (Linearly Elastic Materials) [博升小語] 趕快把 I 的公式背一背吧~

12 Normal Stresses in Beams (Linearly Elastic Materials)
A beam is supported and loaded as shown in the figure. The cross section of the beam is T-shaped as indicated. Take q = 200 lb/ft, Mo =8 k-ft, L=20 ft, and a=2”. (a) Sketch the shear force and bending moment diagrams labeling all significant points and values. (b) Determine the maximum tensile and compressive stresses in the beam (and indicate the location where each acts). Normal Stresses in Beams (Linearly Elastic Materials)

13 Normal Stresses in Beams (Linearly Elastic Materials)
A beam is supported and loaded as shown in the figure. The cross section of the beam is T-shaped as indicated. Take q = 200 lb/ft, Mo =8 k-ft, L=20 ft, and a=2”. (a) Sketch the shear force and bending moment diagrams labeling all significant points and values. Normal Stresses in Beams (Linearly Elastic Materials) X=8

14 Normal Stresses in Beams (Linearly Elastic Materials)
A beam is supported and loaded as shown in the figure. The cross section of the beam is T-shaped as indicated. Take q = 200 lb/ft, Mo =8 k-ft, L=20 ft, and a=2”. (b) Determine the maximum tensile and compressive stresses in the beam (and indicate the location where each acts). STEP 1 : 求斷面資料(和力量無關) Normal Stresses in Beams (Linearly Elastic Materials)

15 Normal Stresses in Beams (Linearly Elastic Materials)
A beam is supported and loaded as shown in the figure. The cross section of the beam is T-shaped as indicated. Take q = 200 lb/ft, Mo =8 k-ft, L=20 ft, and a=2”. (b) Determine the maximum tensile and compressive stresses in the beam (and indicate the location where each acts). STEP 2 : 檢查極值處 Normal Stresses in Beams (Linearly Elastic Materials)

16 Normal Stresses in Beams (Linearly Elastic Materials)
A beam is supported and loaded as shown in the figure. The cross section of the beam is T-shaped as indicated. Take q = 200 lb/ft, Mo =8 k-ft, L=20 ft, and a=2”. (b) Determine the maximum tensile and compressive stresses in the beam (and indicate the location where each acts). STEP 2 : 檢查極值處 Normal Stresses in Beams (Linearly Elastic Materials)

17 Normal Stresses in Beams (Linearly Elastic Materials)
A beam is supported and loaded as shown in the figure. The cross section of the beam is T-shaped as indicated. Take q = 200 lb/ft, Mo =8 k-ft, L=20 ft, and a=2”. (b) Determine the maximum tensile and compressive stresses in the beam (and indicate the location where each acts). STEP 2 : 檢查極值處 Normal Stresses in Beams (Linearly Elastic Materials) Maximum tensile stress: 1715 psi at x = 4 ft, y = -6.5 in Maximum compressive stress: 2144 psi at x = 10 ft, y = -6.5 in

18 重點回顧 [博升小語] 這條公式也是… 「背不出來別說你念過材力!!」的家族成員之一

19 5 6-7 9-10 頁碼 作品 版權圖示 來源/作者 1-20 版權聲明 [李星慧_2014 . 7. _高雄攝影作品]
此圖經同意已進行藍階修改。 您如需利用本作品，請另行向權利人取得授權。 5 國立交通大學機械工程系 鄭文雅 教授，本作品以創用 CC BY-NC-SA 臺灣 3.0 版授權釋出。 6-7 9-10 版權聲明

20 頁碼 作品 版權圖示 來源/作者 12 國立交通大學機械工程系 鄭文雅 教授，本作品以創用 CC BY-NC-SA 臺灣 3.0 版授權釋出。 13 14 18 著作權人 / 肖象權人 皆為 國立臺灣大學 土木工程學系 白博升，本作品以創用 CC BY-NC-SA 臺灣 3.0 版授權釋出。 版權聲明