Review of basic deformations Relations among the shearing force, bending moment and external forces. No- external force segment Uniform-load segment Concentrated force Concentrated couple nal >04g<0 Horizontal straight line Inclined straight line Sudden change from the No changed left to the right eristics Q Q O O O O x O>0O<0 asing functi Q charact inclined straight line Doga Bm the left to Sudden change from Curves the right the left to the right riscs Oppos ite M, x\x x to M M MI M M M 到 beciecasng function tomb-like|bmm M-M=m
Relations among the shearing force, bending moment and external forces. Exter nal forces No- external force segment Uniform-load segment Concentrated force Concentrated couple q=0 q>0 q<0 Charact eristics of Qdiagram Charact eristics of Mdigram C P C m Horizontal straight line x Q Q>0 Q Q<0 x Inclined straight line Increasing function x Q x Q Decreasing function x Q C Q1 Q2 Q1– Q2=P Sudden change from the left to the right x Q C No changed inclined straight line x M x M Decreasing function Curves x M x M Dog-ear from the left to the right Sudden change from the left to the right Opposite x to M M M x M1 M2 Increasing function tomb-like basin- basin M1 − M2 = m
基本氯习 剪力、弯矩与外力间的关系 外无外力段均布教荷段集中力集中力偶 力 0q<0 水平直线 斜直线自左向右突变无变化 Q Q O O O O O Q图特征M图特征 Q>0Q0增函数降函数Q 斜直线 曲线自望右折角自左向右突 Me M M M M MI M 反M 「增函数降函数”坟状盆状折向与P反向M-M2=m
剪 力 、 弯矩与外力间的关系 外 力 无外力段 均布载荷段 集中力 集中力偶 q=0 q>0 q<0 Q 图 特 征 M 图 特 征 C P C m 水平直线 x Q Q>0 Q Q<0 x 斜直线 增函数 x Q x Q 降函数 x Q C Q1 Q2 Q1– Q2=P 自左向右突变 x Q C 无变化 斜直线 x M 增函数 x M 降函数 曲线 x M 坟状 x M 盆状 自左向右折角自左向右突变 与 m 反 x M 折向与P反向 M x M1 M2 M1 − M2 = m
Review of basic deformations pplications of deformations Applications of the strain energy Determine displacements and solve the Determine displacements and solve the statically indeterminate problems. dynamic loading problem. Steps to solve statically indeterminate problems: (1) free falling body: EQuilibrium equations ② Geometric equations- ompatibility equations of de irmiatido+ /1, 2h @Physical equations--relations between the deformation Complementary equations A: Static di splacement of the impact body at the falling point @Solve the equilibrium equations and complementary equations (2) Horizontal impact K
Steps to solve statically indeterminate problems ： ①Equilibrium equations ②Geometric equations——compatibility equations of deformation ③Physical equations——relations between the deformation ④Complementary equations ⑤Solve the equilibrium equations and complementary equations Applications of deformations ： Determine displacements and solve the statically indeterminate problems. Applications of the strain energy ： Determine displacements and solve the dynamic loading problem. j h d K = + + 2 1 1 (1) free falling body : 2 (2) Horizontal impact : j v K d g = △j :Static displacement of the impact body at the falling point
基本氯习 变形的应用: 变形能的应用: 求位移和解决超静定问题求位移和解决动载问题 超静定问题的方法步骤 (1)自由落休 ①平衡方程 2h K,=1+/1+ ②几何方程变形协调方程 ③物理方程变形与力的关系 △产冲击物落点的静位移 ④补充方程 ⑤解由平衡方程和补充方程组 (2)水平冲击 K g|△
超静定问题的方法步骤： ①平衡方程 ②几何方程——变形协调方程 ③物理方程——变形与力的关系 ④补充方程 ⑤解由平衡方程和补充方程组 变形的应用： 求位移和解决超静定问题 变形能的应用： 求位移和解决动载问题 j h d K = + + 2 1 1 (1) 自由落体: g j v d K = 2 (2) 水平冲击: △j:冲击物落点的静位移
Review of basic deformations Materialstesting O MPa b 450 400 350 300 250 200 150 ool op oeol 50 0 0.05 0.10 0.15 0.20gh10.25 E Typical points in the o-2 Curve of the low -carbon steel
M a t e r i a l t e s t i n g sp se ss sb s a b ep et ee st f g h e s(MPa) 0.05 0.10 0.15 0.20 0.25 450 400 350 300 250 200 150 100 50 0 Typical points in the s − Curve of the low – carbon steel p e