上海交通大学：《钢筋混凝土基本原理》课程教学资源（PPT课件）Chapter 6 Members resist axial load plus uniaxial bending

Chapter 6 Members resist axial load plus uniaxial bending (Sections of equivalent eccentrically-loaded short columns)

Chapter 6 Members resist axial load plus uniaxial bending (Sections of equivalent eccentrically-loaded short columns)

讨论： ·偏心受压时，靠近压力和远离压力钢筋 As和As在构件破坏时的应力状态 ·大偏心受压、小偏心受压，区分 。P一M相互作用曲线 ·大偏心受压破坏时，增大压力对构件承 载力的影响

讨论： • 偏心受压时，靠近压力和远离压力钢筋 As’和As在构件破坏时的应力状态 • 大偏心受压、小偏心受压，区分 • P－M相互作用曲线 • 大偏心受压破坏时，增大压力对构件承 载力的影响

6.1 Axial load plus bending at ultimate limit state The combination of an axial force N and bending moment Mis equivalent to the axial load N applied at an eccentricity(偏心距)e. Equivalent Bending and axial load eccentrically loaded column Section N Section subjected to bending and axial load

6.1 Axial load plus bending at ultimate limit state The combination of an axial force N and bending moment M is equivalent to the axial load N applied at an eccentricity（偏心距） e. Section subjected to bending and axial load

Uniaxia及Bendin9 Bax心a2 Aending Uniaxial bending and biaxial bending

Uniaxial bending and biaxial bending

(e) () (a) (b) (c) (d) (a)eo=0 (b)eo<ecor (c)ecor<eo<eob (d)eo=eob (e)eo-eob (f)eo=oo ecor一截面核心距 eob—balanced eccentricity(界限偏心距) The above Fig.represents the cross-section of a member with typical strain and stress distributions for varying eccentricities eo

• The above Fig. represents the cross-section of a member with typical strain and stress distributions for varying eccentricities e0 (a) e0=0 (b) e0e0b (f)e0=∞ ecor——截面核心距 e0b——balanced eccentricity (界限偏心距)

Two failure modes ·Compression failure At failure The reinforcements at tensile zone do not yield in tension eo56 E,Ey

Two failure modes • Compression failure • Tension failure At failure At failure The reinforcements at tensile zone do not yield in tension e0e0b    b s y    s y   

A,=A.f do-(d0= 以上分析是基于A,=A,,若配筋量很大或很小，都会引起 failure mode的变化，如：偏心距较大，但是拉区配筋过大， 不屈服，变成压坏柱

以上分析是基于 ， 若配筋量很大或很小，都会引起 failure mode的变化， 如：偏心距较大，但是拉区配筋过大， 不屈服，变成压坏柱。 ' As  As

6.2 Analysis and design of columns (N compression) ·Basic assumptions same as that in pure bending Conditions of compatibility same as that in pure bending Equilibrium equation T+C=T+N M=CZ+T(ho-a)-N(e+h/2-as) The equivalent rectangular block same as that in pure bending

6.2 Analysis and design of columns （N compression) • Basic assumptions same as that in pure bending • Conditions of compatibility same as that in pure bending • Equilibrium equation ( ) ( / 2 ) ' 0 ' ' M CZ T h a N e h as T C T N          • The equivalent rectangular block same as that in pure bending

界限相对受压区高度ξb same as that in pure bending same as that in pure bending s 受拉区钢筋有可能屈服，有可能不屈服) when X≤Xb os =Jy X Xub o,<∫ h-1.25x 1.25x 0.8

'  s same as that in pure bending  s when ub x  x s y   f ub x  x s y   f s s s uEs x h x   E  1.25 0 1.25   （受拉区钢筋有可能屈服，有可能不屈服） 1) 0.8  (     s u 界限相对受压区高度ξb same as that in pure bending

The approximate stress Os in over reinforced section 6☒0) 2000 行保代血贸高用受 导容 1000 0.81.6东 0 0.20.40.6 1.0i.2 88 8 5340 -0.0033E(3-) 5b=0.528 -1000F 8=合03 ￡-0.8 -f0.8 5-0.8 2000- Test result show:when0.8 , 0.8

Test result show：when   0.8 1) 0.8  (     s u The approximate stress  s in over reinforced section