Chapter 5 Members resisting bending
Chapter 5 Members resisting bending
● 5.1 Behavior 5.1.1 Behavior of singly reinforced beam 应变计 。位移计吊 f (a) (b) (c) (d) (e) (f) (g) MMcr My >My Mu M<Mu
• 5.1 Behavior 5.1.1 Behavior of singly reinforced beam MMcr My >My Mu M<Mu
录相资料 > Under reinforced beam Over reinforced beam
录相资料 Under reinforced beam Over reinforced beam
对 1/P a~b before cracking b cracking d yield of rebar f ultimate load capacity
a～b before cracking b cracking d yield of rebar f ultimate load capacity
5.2 Analysis methods 5.2.1 Basic assumptions .Plane cross section remain plane during bending(Bernoulli assumption) .There is full bond between concrete and steel .Concrete behavior in the compressive zone is described by an uniaxial stress-strain curve .The tensile strength of concrete is ignored .The behavior of steel is described by the stress-strain curves for steel in compression or tension .Failure accurse when the strain of concrete of the extreme compressive fiber attains a critical value su usually taken to be equal to 0.0033
5.2 Analysis methods • 5.2.1 Basic assumptions •Plane cross section remain plane during bending (Bernoulli assumption) •There is full bond between concrete and steel •Concrete behavior in the compressive zone is described by an uniaxial stress-strain curve •The tensile strength of concrete is ignored •The behavior of steel is described by the stress-strain curves for steel in compression or tension •Failure accurse when the strain of concrete of the extreme compressive fiber attains a critical value εu usually taken to be equal to 0.0033
5.2.2 Conditions of equilibrium and compatibility Material law for concrete fs $工 C=[bu dv T=AM Ibucydy (IX=X- M C T=Aly Strain Internal stresses Internal actions External action distribution Material law for steel
5.2.2 Conditions of equilibrium and compatibility
Compatibility equations ho-XaEu a E T -a Xa C Es Z ho 1 ho T Equilibrium equation T+C=T M=CZ+T(ho-a)
Compatibility equations u a a s x h x 0 u a a s x x a ' ' 1 0 h u s s 's u xa 0 h Equilibrium equation ( ) ' 0 ' ' M CZ T h a T C T C Z T’ T
5.2.3 The equivalent rectangular block The actual distribution of the compressive stress in a section has the form of a rising parabola.It is time consuming to evaluate the volume of the compressive stress block if it has a parabolic shape.An equivalent rectangular stress block can be used with ease and without loss of accuracy to calculate the compressive force and hence the flexural moment strength of the section
5.2.3 The equivalent rectangular block • The actual distribution of the compressive stress in a section has the form of a rising parabola. It is time consuming to evaluate the volume of the compressive stress block if it has a parabolic shape. An equivalent rectangular stress block can be used with ease and without loss of accuracy to calculate the compressive force and hence the flexural moment strength of the section
A (a) (b) (c) (d) 图1413.极限状态和等效矩形应力图 (a)截面(h)截面应变(c)应力(d)等效矩形挂应力图 矩形应力图的受压区高度x可取等于按截面应变保持平面的假定所确定的中和轴高度乘以 系数B。当混凝土强度等级不超过C50时.B取为0.8，当混凝土强度等级为C80时，B取 为0.74，其间按线性内插法确定。 矩形应力图的应力值取为混凝土轴心抗压强度设计值f乘以系数1。当混凝土强度等级不 超过C50时，a取为1.0，当混凝土强度等级为C80时，a1取为0.94，其间按线性内插法确定
f c a1f c 矩形应力图的受压区高度x可取等于按截面应变保持平面的假定所确定的中和轴高度乘以 系数β。当混凝土强度等级不超过C50时．β取为0.8，当混凝土强度等级为C80时，β取 为0.74,其间按线性内插法确定。 矩形应力图的应力值取为混凝土轴心抗压强度设计值f c乘以系数a1。当混凝土强度等级不 超过C50时，a1取为1.0，当混凝土强度等级为C80时，a1取为0.94，其间按线性内插法确定
·ACI B=0.85-0.008(f。-30) fm=0.85f f&=0.79fcm fem =0.67fcu
• ACI 0.85 0.008( 30) ' f c ' cm 0.85 c f f c cu f 0.79 f ' cm cu f 0.67 f