National Taiwan University Material Mechanics Chapter Five Stresses

National Taiwan University Material Mechanics Chapter Five Stresses in beams 2014 Summer 國立臺灣大學土木 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】 Material Mechanics 2014 SUMMER

Stresses in beams Class 1. Class 2. Class 3. Class 4. Class 5. TOPIC KEYPOINT PAGE Introduction Pure bending & Non-uniform bending Curvature of a beam Longitudinal Strains in Beams Normal Stresses in Beams (Linearly Elastic Materials) Class 6. Design of Beams for Bending Stresses Class 7. Shear Stresses in Beams of Rectangular Cross Section Class 8. Shear Stresses in Beams of Circular Cross Section Class 9. Shear Stresses in the Webs of Beams with Flames Class 10. Built-Up Beams and Shear Flows 2 Material Mechanics 2014 SUMMER

Class 7 Shear Stresses in Beams of Rectangular Cross Section TOPIC KEYPOINT PAGE 3 Material Mechanics 2014 SUMMER

剪力流的概念 利用這個 TOPIC Shear Stresses in Beams of Rectangular Cross Section 來求這個 KEYPOINT PAGE 4 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT PAGE 5 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT (先別去管向量的問題) PAGE 6 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT PAGE 7 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT PAGE 8 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT PAGE 9 Material Mechanics 2014 SUMMER

又 TOPIC Shear Stresses in Beams of Rectangular Cross Section If the shear stress are uniformly distributed across the width b of the beam KEYPOINT [注意] 這個關係式雖然簡單，但卻時常忘記 PAGE 10 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT 這頁完全是 重‧點‧啊!!! PAGE 11 Material Mechanics 2014 SUMMER

TOPIC KEYPOINT PAGE 12 Material Mechanics 2014 SUMMER

TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT PAGE 13 Material Mechanics 2014 SUMMER

這個分佈的圖形也是重點 TOPIC Shear Stresses in Beams of Rectangular Cross Section KEYPOINT 這個數值反而沒那麼重點… PAGE 14 Material Mechanics 2014 SUMMER

Limitation of the shear formula: n n n TOPIC Shear Stresses in Beams of Rectangular Cross Section n n KEYPOINT PAGE Linearly elastic materials with small deflections Applied only to prismatic beams The edges of the cross section must be parallel to the y axis (therefore, the formula is not applicable to sections of triangular or semicircular shape) The shear stresses must be uniform across the width of the cross section The accuracy depends upon the height-to-width ratio of the cross section. For square section (b=h), the true maximum shear stress is about 13% greater than the value given by the shear formula introduced in this section. 15 Material Mechanics 2014 SUMMER

重點回顧 TOPIC KEYPOINT PAGE 16 [材力小語] 務必熟練Q的計算…其實是有小撇步的XD Material Mechanics 2014 SUMMER

頁碼 作品 版權圖示 R. C. Hibbeler, “Mechanics of Materials”, 7 th Ed. Pearson Prentice-Hall 2008. P 385、P 386。 本作品依據著作權法第 46、52、65 條合 理使用。 12 TOPIC 來源/作者 版權聲明 KEYPOINT PAGE 19 Material Mechanics 2014 SUMMER