# 202.121.48.120b70c3b42-49ac-47d2-88a2-9867279132b

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§2-5     拉（压）杆内的应变能

§2-5   Strain Energy in the Axially
应变能（Strain Energy）:
伴随着弹性变形的增减而改
变的能量
V

V  W       2-8

功能定理

F
F
F
F

F

F
l                 l
l1
O               l
1     1
W  FL  FN L              FN L
2     2              L                     l
EA
1           FN2 L
V  FN L                    2-9
2           2 EA
1        2-10

V   2      1
v             
Density): 单位体积内的应变                         V      AL   2
          图示的杆系是由两根圆截面钢杆铰接而成。已知

2.12       弹性模量E＝2.1×105MPa，设在结点A处悬挂一重
物F＝100kN，试求结点A的位移δA。
X 0               FNAC sin   FNAB sin   0
FNAC  FNAB 
F
B     1         2    C     Y  0           FNAC cos   FNAB cos   F  0
2 cos 
FNAB FNAC
α α              LAB  LAC        
FNAC L

FL
EA      2EA cos 
A
  LAC 
FL
A                                A  AA
                       cos     2EA cos 2 
F                     A          1.3mm 100 103  2

LAC                                         
LAB   2  2.1105 106         252 10 6  cos 300
4

A
小结

REVIEW
Stiffness (Robert Hooke, 1648)

Robert Hooke was the first to experiment
with and define the stiffness of materials.
He suspended various masses from
springs, and measured the extension.

The force is proportional to
the extension of the spring.

m
u
Material Properties (Thomas Young, 1810)

Thomas Young helped to develop the
theory of how materials deform elastically.
In particular, he defined an important
material constant, “Young’s Modulus”.

P                                           P

L
Internal Normal Force
Let Axial Stress,  
(in Units of N/m2
C.S. Area                 or Pascals (Pa))

Change in Length
Let Axial Strain,                                (Dimensionless)
Original Length
Material Properties (Cont.) (Simon Poisson, 1825)
theories about lateral deflections of materials.

When a bar is placed in tension, lateral
contractions accompany the extension.

Initial
Shape
Final
Shape                                        P    A real math nut.

P

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