①Analysis of external forces：External forces are
reduced along the centroid of section and resolved along principal axes of inertia.
②Analysis of internal forces：Determine the internalforce equation and its diagram corresponding to each external force component and the critical section.
Mechanics of Materials
Chapter 9
Composite deformations
1
2
CHAPTER 9 COMPOSITE DEFORMATIONS
Skew a.斜交的
§9–1 SUMMARY
§9–2 SKEW BENDING
§9–3 COMBINATION OF BENDING AND
③Analysis of stresses：Plot the distribution
diagram of the stress in the critical section，do the superposition of the stresses and establish the strength condition of the critical point.
力
M y M cos j
Pz z
4
§9–1
SUMMARY
1、Composite deformation：
Structural members will produce several types of simple deformations when subjected to complex external loads . The stress corresponding to each simple deformation can not be neglected when the magnitude of each stress has the same order . This kind of deformation is called the composite deformation .
M z Py ( L x) P( L x) sinj M sinj
m z
x Pz P
M y M cos j
j
P
Pz
z
x y
m
L
Py
Py
y
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解：1.将外载沿横截面的形心主轴分解 2.研究两个平面弯曲 ① 内
Py Psinj
Pz Pcos j
M z Py ( Lx) P( Lx)sinj M sinj
in the same plane.
transversal 横向的
2、Methods to study the skew bending：
1).Resolve：Resolve the external load along two centroid principal axes of inertia of the cross section and get two perpendicular planar bending .
P
R M P
P
z x
y
5
§9–1
概 述
一、组合变形 ：在复杂外载作用下，构件的变形会包含几种简
单变形，当几种变形所对应的应力属同一量级时，不能忽略
之，这类构件的变形称为组合变形。 P P
R
M P y
z x
6
P
hg
7
P
hg
8
P q
hg
Dam
9
P q
hg
水坝
10
2、Methods to study composite deformations— Principle of superposition
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二、组合变形的研究方法 —— 叠加原理 ①外力分析：外力向形心(或弯心)简化并沿形心主惯性轴分解; ②内力分析：求每个外力分量对应的内力方程和内力图，确
定危险面。
③应力分析：画危险面应力分布图，叠加，建立危险点的强 度条件。
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§9–2 SKEW BENDING transverse 横向的 1、Skew bending：After bending deformation , the deflection curve and the external forces（transversal forces） of the rod are not
TORSION
§9-4 BENDING AND TENSION OR COMPRESSION ECCENTRIC TENSION OR COMPRESSION KERNEL OF THE SECTION
3
第九章 组合变形
§9–1 概述
§9–2 斜弯曲
§9–3 弯曲与扭转的组合
§9-4 拉(压)弯组合 偏心拉（压） 截面核心
z x Pz
j
P
Pz
Py
z
Py2.叠加：对两个平面弯曲进行研究；然后将计算结果叠加起来。
z x Pz
j
P
Pz
Py
z
Py
y
P
y
Solution：1.Resolve the external force along the centroid principal axis of inertia of the cross section Py Psinj Pz Pcos j 2.Study the bending in two planes : ①Internal forces
z P
j
Pz
z x
Py
y y Pz P Py
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§9–2 向力）不共面。 二、斜弯曲的研究方法 ：
斜弯曲
一、斜弯曲：杆件产生弯曲变形，但弯曲后，挠曲线与外力（横
1.分解：将外载沿横截面的两个形心主轴分解，于是得到两个正交 的平面弯曲。
z P
j
Pz Py y
z x Pz y P
Py
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2).Sum：Analyze bending in two perpendicular planes and sum the results of the calculation.