Chapter 8 Torsion
Chapter 8 Torsion
1 Sections Sub jected to Torsion precast column with recess (b)Precast spandrel beam truck loading (c)Eccentrically loaded box-girder bridge (d)Curved guideway structure
8.2 Basic elastic behavior of sections subjected to torsion Circular sections Plane section before torsion remain plane after torsion Te TR tmax T= I,—Polar moment of inertia(极惯性矩) 元R4 TR 2T. T 1。= max 2 I。zR W W Torsional elastic section modulus(受扭弹性抵抗矩) W。= 2
8.2 Basic elastic behavior of sections subjected to torsion Circular sections Plane section before torsion remain plane after torsion 0 TeR I I 0——Polar moment of inertia (极惯性矩) 2 4 0 R I te e e e W T R T I T R 3 0 max 2 Wte ——Torsional elastic section modulus （受扭弹性抵抗矩） 3 2 Wte R τmax R Te
·Rectangular section Warping(翘曲) Plane section does not remain plane after torsion. There exist axial stress as well as circumferential(圆周向的) shear stress 2 T。 T max ab'h Wre We一Torsional elastic section modulus.(受扭弹性抵抗矩) h/b 1 1.2 1.5 0。 0.208 0.219 0.231
• Rectangular section Warping (翘曲) Plane section does not remain plane after torsion. There exist axial stress as well as circumferential （圆周向的） shear stress te e e e W T b h T max 2 Wte—Torsional elastic section modulus. (受扭弹性抵抗矩) h/b 1 1.2 1.5 αe 0.208 0.219 0.231
8.3 Basic plastic behavior of rectangular section subjected to torsion 7力 1 T 》 ( (n) T。 max b2(3h-b) W。。b(6h-) 6 Torsinal plastic section modulus(抗扭塑性抵抗矩)
8.3 Basic plastic behavior of rectangular section subjected to torsion (3 ) 6 1 2 max b h b TP (3 ) 6 1 2 Wtp b h b Torsinal plastic section modulus（抗扭塑性抵抗矩）
Sand-heap analogy
Sand-heap analogy
b 2 T=b(3h-b加 h 6 b Let 45° 1go=Tmax 2 b 2 max bb 2 b· r+6(- 22 2 6 (-)(3h-6)5mm 2 T,=2V W max
max tg m a x m a x 1 1 2 3 2 2 2 2 b b b V b b h b 3 2 2 m a x m a x m a x 1 1 1 3 6 4 1 2 b b h b b h b T p 2V Wtp V max 2 h θ b max 2 b 2 b 2 b 45° Let max 2 (3 ) 6 1 T p b h bτ
Calculation methods for T section and section w =W+W+W 分块原则：尽量保证较宽块体的完整性
Calculation methods for T section and 口section ' Wt Wtw Wtf Wtf 分块原则：尽量保证较宽块体的完整性
