10.33拉压变形杆件内部的神奇世界横截面的正应力

section is uniform.
A
3. Phenomena for the deformation and plane assumption
ab cd
F
a´
b´
F
c´
d´
Plane assumption：all cross sections remain plane
after deformation。
F -50kN
Solution
F F -150kN
Find the internal force first FN1=-50kN FN2=-150kN
1000 1000
240×240 370×370
We get the axial-force diagram as shown on the left.
1000 1000
F -50kN F F -150kN
240×ess over the cross
section of column I is
1
FN1 A1
50103 N (240mm) (240mm)
0.87MPa
(compression)
For column II:
2
FN 2 A2
150103 N (370mm) (370mm)
1.1MPa (compression)
center of the free-body; Otherwise it is negative.
´
a
b
c ´ d
2. Stress on the cross-section of axially loaded bar
F
F
F FN(x)
s
FN (x)
dA
A
Assume: stress on the cross- FN (x)
• Normal stress; • Positive when it is a pulling (or tensile) ; • Negative when it is a pressure (or compressive) ;
σ
σ
σ
σ
Shear stress
Positive when it tends to rotae clockwise relative to the
stress on the cross-section is uniform.
Example
Determine the maximum working stress of the square brick column
under the loads. It is known that F=50kN.
3
Stress in an Axially Loaded Bars
1. The concept of Stress
F q F /l
l F 2l
F
+ –
F
F
l
F
+
The strength of axially loaded bar
axial forces properties of the cross sections strength of materials
• General case
F
F3
A
F2
F2
F1
F1
p: Internal force intensity pAlim 0FA ddFA
1Pa=1N/m2 1GPa 109 Pa 1MPa=106Pa
p
F3
k
Normal stress
Shear stress
p2 2 2
Sign Conventions
Review
F F
强度问题 strength
F
Tension and
F
Compression
刚度问题 stiffness
问题的提出
这是小你杆明件们和受小认力红为平，此衡两处时个于人杆静用件止力的状相态内等， 时部的是情什况。么状态呢？
2
用力过大杆件本身就会坏掉。
在这里用“假想截面” 就会很方便！