《材料力学》（双语版） 第五章 弯曲应力

Mechanics of materials BENDI

1 Mechanics of Materials

材料力 五应为

2

CHAPTER 5 STRESSES IN BENDING §5-1 FORWORD DIs5-2 NORMAL STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING D85-3 SHEARING STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING S85-4 STRENGTH CONDITIONS OF THE NORMAL STRESS AND SHEARING STRESS OF THE BEAM. REASONABLE SECTION OF THE BEAM D85-5 PLANAR BENDING OF UNSIMMETRIC BEAM BENDING CENTER OF THE OPENED THIN-WALLED SECTION D 85-6 LIMIT BENDING MOMENT OF A MATERIAL WITH PLASTICITY CONSIDERED

3 §5–1 FORWORD §5–2 NORMAL STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING §5–3 SHEARING STRESS ON THE CROSS SECTION OF THE BEAM IN PLANAR BENDING §5–4 STRENGTH CONDITIONS OF THE NORMAL STRESS AND SHEARING STRESS OF THE BEAM  REASONABLE SECTION OF THE BEAM §5–5 PLANAR BENDING OF UNSIMMETRIC BEAMBENDING CENTER OF THE OPENED THIN-WALLED SECTION §5–6 LIMIT BENDING MOMENT OF A MATERIAL WITH PLASTICITY CONSIDERED CHAPTER 5 STRESSES IN BENDING

第五章弯曲应力 §51引言 □§5-2平面弯曲时梁横截面上的正应力 □§53梁横截面上的剪应力 §54梁的正应力和剪应力强度条件·梁的合理截面 □§55非对称截面梁的平面弯曲·开口薄壁截面的弯曲中心 □§56考虑材料塑性时的极限弯矩

4 §5–1 引言 §5–2 平面弯曲时梁横截面上的正应力 §5–3 梁横截面上的剪应力 §5–4 梁的正应力和剪应力强度条件 梁的合理截面 §5–5 非对称截面梁的平面弯曲开口薄壁截面的弯曲中心 §5–6 考虑材料塑性时的极限弯矩 第五章 弯曲应力

STRESSESINBENDING §5-1 FORWARD M I\(Internal forces)stresses on the cross section of the bending member Shearing force 0 Shearing stress t Internal foxs( ing moment M→ normal stress

§5－１ FORWARD 1、(Internal forces) stresses on the cross section of the bending member Internal forces Shearing force Q Shearing stress t Bending moment M Normal stress s

意画应 §5-1引言 M 1、弯曲构件横截面上的(内力)应力 剪力Q一剪应力τ 内力 弯矩M→正应力

§5－１ 引言 1、弯曲构件横截面上的（内力）应力 内力 剪力Q 剪应力t 弯矩M 正应力s

STRESSESINBENDING 2、 Study method There are only normal stresses in the section under plane bending-beam of pure bending (There is only M and no Q in the cross section) There are shearing stresses in the section under plane bending-beam of transverse bending. (There areQ and m in the cross section) Such as: P Longitudinal plane of symmetr

There are only normal stresses in the section under plane bending beam of pure bending (There is only M and no Q in the cross section). There are shearing stresses in the section under plane bending beam of transverse bending. (There are Q and M in the cross section). 2、Study method Longitudinal plane of symmetry Such as： P1 P2

意画应 2、研究方法 平面弯曲时横截面σ→纯弯曲梁(横截面上只有M而无Q的情况) 平面弯曲时横截面τ一~剪切弯曲(横截面上既有Q又有M的情况) 例如: P 纵向对称面

平面弯曲时横截面s 纯弯曲梁(横截面上只有M而无Q的情况) 平面弯曲时横截面t 剪切弯曲(横截面上既有Q又有M的情况) 2、研究方法 纵向对称面 例如： P1 P2

STRESSESINBENDING P Pure bending: A B Deformation of some portion of the ●● beam in which there are only bending moment and no shearing stress is called 70 pure bending. Such as portion AB M、 P 纯弯变形几何关系

Deformation of some portion of the beam in which there are only bending moment and no shearing stress is called pure bending. Such as portion AB. a P P a A B Q M x x Pure Bending: P P Pa

意画应 P 纯弯曲( Pure Bending A B ●● 某段梁的内力只有弯矩 没有剪力时,该段梁的变 形称为纯弯曲。如AB段。 M、 P 纯弯变形几何关系

某段梁的内力只有弯矩 没有剪力时，该段梁的变 形称为纯弯曲。如AB段。 a P P a A B Q M x x 纯弯曲(Pure Bending): P P Pa