材力小结

1．Three requirements for members are strengt , stiffness and stability.

2．Three basic assumption for deformable solid are continuity assumption, homogenization assumption（均匀性假设） and isotropy assumption（连续性假设）.

3．Materials are assumed to be continuous, homogeneous , isotropic, linearly elastic （线性弹性）and small deformation.

4．Stress means force per unit area.

5．Stresses are classified into normal stresses and shear stresses

6．For normal stresses: positive in tension and negative in compression

7．For shear stresses: positive in clockwise direction and negative in counterclockwise direction.

8．Stresses have a unit of Pa, kPa, or MPa.

9．Stress and strain curve can be obtained from laboratory testing.

10．Stress and strain curve has four stages: elastic stage ,yielding stage, strengthing stage and stage of local deformation（局部变形阶段） .

11．From stress and strain curve, we get Young’s modulus(modulus of elasticity), elastic limit（弹性极限）, yielding strength （屈服极限）and ultimate strength（强度极限）.

12．According to the permanent deformation before failure, materials can be classified as ductile materials（塑性材料） and brittle materials（脆性材料）.

13．Hooke’s law in simply tension states that the longitudinal stress is linearly proportional to the longitudinal strain

14．Hooke’s law in pure shear states that the shear stress is linearly proportional to the shear strain.

15．Modulus of elasticity or Young’s modulus

16．Shear modulus（切变模量） of elasticity or modulus of rigidity can be derived from modulus of elasticity and Poisson's ratio.

17．Poisson's ratio is defined as the absolute value of the lateral strain(横向线应变) over axial strain(纵向线应变).

18．Poisson's ratio ranges from 0 to 0.5 generally.

19．Shear strain（切应变） is an angle change produced by the shear stresses（切应力）.

20．Normal strain is the elongation per unit length.

21．Internal force is acting on a certain cross section.

22．Internal force can be solved from external forces with the help of free-body diagram.

23．Internal force is usually displayed in a diagram.

24．Internal force diagram shows clearly the distribution of the internal force, which helps us to locate the critical cross section（危险截面） and calculate the maximum stress.

25．Stresses on the inclined cross section changes with the normal direction of the cross section.

26．Maximum normal stresses occur when shear stresses become zero.

27．Maximum shear stresses occur when normal stresses become average.

28．The strain energy stored in a member is equal to the work done by the external force acting on the same member.

29．The strain energy is expressed in the form of strain and stress.

30．Statically equivalent forces produce big difference of stress state in the nearby region of forces, little

difference of stress state in the region far from the action of the forces.

31．Statically equivalent forces mean that two systems of forces have the same resultant force and same resultant moment.

32．Parallel planes in the member keep parallel after deformation.

33．Each point on the plane has the same elongation or contraction(收缩).

34．Thus ,the strain on the plane is a constant.

35．Planes in the shafts rotates（旋转） with each other.

36．The distance of planes remain unchanged.

37．The shear strain is dependent on the angle of twist per unit length and linearly proportional to the distance from the center.

38．The determination of a factor of safety must take into account the matters as the following:

39．1]Imperfect manufacture（非完美产品） 2]Uncertainty of loading（不确定荷载）

40．3]Approximate theory 4]Testing methods

41．5]Consequence of failure（minor damage or major catastrophe） 6]Environmental effects

42．7]Economic consideration and so on.

43．Beam 梁

44．Simply supported beam 简支梁

45．Roller support of pin joint 可动铰支座 Fixed suppert of pin joint 固定铰支座

46．Cantilever <?kæntili?v?>beam 悬臂梁 Fixed end 固支端

47．Bending moment diagram 弯矩图

48．Shearing force diagram 剪力图

49．Uniformly distributed force 均布力

50．differential equation of the deflection curve 挠曲线微分方程

51．bending moment equation 弯矩方程

52．shear force equation 剪力方程

53．load equation 荷载方程

54．boundary condition 边界条件

55．continuity condition 连续条件(连接条件)

56．symmetry condition 对称条件

57．Statically determinate problems (静定问题) are problems in which the reaction forces can be determined by the equilibrium equations only.

58．Statically indeterminate problems (静不定问题) are problems in which the reaction forces can not be determined without the introduction of the coordinate relations.

59．Measures for reducing the bending stresses are 1) increasing the moment of inertia of a cross section, 2) adjustment of the supports and load, 3) rational design of cross section.

60．What is the difference between the strength condition or criterion and the stiffness condition or criterion?

61．What is the plane hypothesis for the pure bending?

62．What is the limitation of the normal stress and shear stress formula for a beam?

63．How many steps are involved in the method of successive integration?

64．What does the principles of superposition for the deflection of a beam state?

65．What is neutral axis of a beam, how to determine it?

66．How is the shear stress distributed on the cross section of a beam?

67．How is the normal stress distributed on the cross section of a beam?

68．Is the normal strain distribution on the cross section dependent on the materials of a beam?

69．Find the deflection at the end of the cantilever beam supported by a spring at the middle of the beam as shown in figure 1. The rigidity of the beam is EI.

70．Find the neutral axis of a beam made of two materials E1 / E2=3, as shown in figure 2.

71．What is the application of shear force diagram and moment diagram?

72．What is the difference between the strength condition or criterion and the stiffness condition or criterion?

73． Stress state 应力状态

74． Mohr‘s circle for stress 应力莫尔圆

75． Principal stress 主应力

76． Maximum shear stress 最大剪应力

77． Octagonal shear stress 八面体剪应力

78．Statically determinate problems (静定问题)

79． are problems in which the reaction forces can be determined by the equilibrium equations only.

80．Statically indeterminate problems (静不定问题) are problems in which the reaction forces can not be determined without the introduction of the coordinate relations.

81．In three dimensional problems, there exist 6 independent stress components, they are __ __ __ __ __ and __ respectively.

82．

83．In two dimensional problems, there exist 3 independent stress components, they are

84． ___ ___ and ___ respectively.

85．The four classical strength theories include maximum tensile stress theory maximum elongated normal strain theory maximum shear stress theory and maximum distortional strain energy theory. The first and second are mainly for brittle materials; the third and fourth are mainly for ductile materials.

86．How to construct the Mohr's circle for stress?

87．What can we get from the Mohr's circle for stress?

88．Make a brief comparison between the four strength theories

89．组合变形及连接部分的计算 combined deformation analysis of connections

90．连接件 connecting elements 键key 螺栓bolt 铆钉rivet

91．工程实用计算方法 engineering method of practical analysis

92．交变应力 alternating stress

93．挤压力 bearing force

94．计算挤压面积 effective bearing surface

95．总应力 overall stress

96．榫接 mortise joint 榫头 Tenon 榫眼mortise

97．榫接 joggle connection

98．焊接 welded joint

99．Find the deflection at the end of the cantilever beam supported by a spring at the middle of the beam as shown in figure 1. The rigidity of the beam is EI.

100．Find the neutral axis of a beam made of two materials E1 / E2=3, as shown in figure 2.

101．What is the plane hypothesis for the pure bending?

102．What is the limitation of the normal stress and shear stress formula for a beam?

103．How to plot shear force diagram and moment diagram?

104．What are static moment and moment of inertia of cross sectional area used for ?

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