National Taiwan University Material Mechanics Chapter Four Shear

National Taiwan University Material Mechanics Chapter Four Shear Forces and Bending Moments 2014 Summer 國立臺灣大學 土木 程學系 1 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

Introduction TOPIC KEYPOINT PAGE 2 Material Mechanics 2014 SUMMER

Fixed Hinge TOPIC Shear Forces and Bending Moments KEYPOINT 每種support 對應的reactions PAGE Roller With 2 dimension： Fixed supports Hinge supports Roller supports → 3 reactions(2 forces + 1 moment) → 2 reactions(2 forces) → 1 reaction (1 force) 3 Material Mechanics 2014 SUMMER

TOPIC Shear Forces and Bending Moments KEYPOINT 每種代號 代表的載重形式 PAGE With 2 dimension： P ：Concentrated forces M：Concentrated moments q ：Distributed forces, note that 4 Material Mechanics 2014 SUMMER

+ + TOPIC Shear Forces and Bending Moments With 2 dimension： KEYPOINT 每種vector 慣用的正負號定義 PAGE q V M 5 Material Mechanics 2014 SUMMER

Relations Between… Loads, Shear Forces and Bending Moments TOPIC KEYPOINT PAGE 6 Material Mechanics 2014 SUMMER

For a beam under general loadings: TOPIC Relations Between… q&V&M KEYPOINT PAGE 7 Material Mechanics 2014 SUMMER

Take an arbitrary infinitesimal element of length dx TOPIC Relations Between… q&V&M KEYPOINT PAGE 8 Material Mechanics 2014 SUMMER

TOPIC Relations Between… q&V&M Considering that this element should be in equilibrium KEYPOINT PAGE 9 ←重要!!! Material Mechanics 2014 SUMMER

以這個平面來進行推導 TOPIC Relations Between… q&V&M Considering that this element should be in equilibrium 省略 KEYPOINT PAGE 10 ←重要Again!!! Material Mechanics 2014 SUMMER

重點回顧 TOPIC drawing V&M diagrams KEYPOINT PAGE 11 [博升小語]瞬間畫出q&V&M可是土木系必備技能之一…(茶 且聽下回分解 Material Mechanics 2014 SUMMER