长沙理工大学：《结构设计原理》课程教学资源（PPT课件）Chapter 6 Carrying Capacity of Members under Axial Loading 轴心受压构件承载力计算

JPKIC 结构设计原理 Teprimepledtstmicturgdesign Chapter 6 轴心受压构件承载力计算 Calculation to Carrying Capacity of Members under Axial Loading

Chapter 6 轴心受压构件承载力计算 Calculation to Carrying Capacity of Members under Axial Loading

JPKic 箱构试原黑 Main content of this chapter ● With a longitudinal axis of steel stirrups and the general failure mode of compression members,bearing capacity; Longitudinal and spiral reinforcement with stirrups failure modes of axial compression members,bearing capacity; The concept of stability factor and its influencing factors; Analysis of the core concrete strength and strength calculation; Ordinary hoops column,spiral column reinforcement stirrup features and construction requirements

Main content of this chapter ● With a longitudinal axis of steel stirrups and the general failure mode of compression members, bearing capacity; ● Longitudinal and spiral reinforcement with stirrups failure modes of axial compression members, bearing capacity; ● The concept of stability factor and its influencing factors; ● Analysis of the core concrete strength and strength calculation; ● Ordinary hoops column, spiral column reinforcement stirrup features and construction requirements

JPKIC 结构设计原理 Theprinepletstrmicturgdesign 6.1 with a longitudinal axis of the stirrup steel bar and the general com pression member 1.Classification of reinforced concrete columns Ordinary hoops column:longitudinal reinforcement and stirrups with the column,(Figure 6-1a). oSpiral hoop column:with a longitudinal reinforcement and spiral reinforcement rings or bars welded column,(Figure 6-1b). Of which:to help compression longitudinal reinforcement,bending away from the commitment to prevent brittle failure.Spiral reinforcement component to improve strength and ductility

§ 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member 1.Classification of reinforced concrete columns ⚫ Ordinary hoops column: longitudinal reinforcement and stirrups with the column, (Figure 6-1a). ⚫ Spiral hoop column: with a longitudinal reinforcement and spiral reinforcement rings or bars welded column, (Figure 6-1b). Of which: to help compression longitudinal reinforcement, bending away from the commitment to prevent brittle failure. Spiral reinforcement component to improve strength and ductility

JIPKIC 构试原黑 S 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member B) 纵向钢筋 纵向钢筋 箍筋 螺旋箍筋 Figure 6-1 axis of two reinforced concrete compression members a)ordinary hoops column b)screw hoops column

 纵向钢筋   ) 纵向钢筋 箍筋   螺旋箍筋 )  Figure 6-1 axis of two reinforced concrete compression members a) ordinary hoops column b) screw hoops column § 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member

IPKIC 结构设计原理 6.1 with a longitudinal axis of the stirrup steel bar and the genera compression member 2.Failure modes 1)factors: (1)creep: So that the sudden increase of steel stress,concrete stress reduction (stress re-distribution) Sudden unloading of concrete will have tensile stress. (2)The slenderness ratio:(lo/b) 2)Failure of ordinary hoops column (1)short column damage -material damage. Failure characteristics:longitudinal cracks,longitudinal reinforcement muster, concrete crack. (2)destruction of long columns -unstable failure Failure characteristics:first,the concave side was crushed concrete,concrete surface longitudinal cracks;convex side of the pressure suddenly changed from tension,transverse cracks appear;destruction before the horizontal deflection increased rapidly rather sudden destruction come,leading to instability Damage Carrying capacity is less than the same cross section,reinforcement,material columns

2. Failure modes 1) factors: (1) creep: ●So that the sudden increase of steel stress, concrete stress reduction (stress re-distribution) ●Sudden unloading of concrete will have tensile stress. (2) The slenderness ratio: (l0/b) 2) Failure of ordinary hoops column (1) short column damage - material damage. Failure characteristics: longitudinal cracks, longitudinal reinforcement muster, concrete crack. (2) destruction of long columns - unstable failure Failure characteristics: first, the concave side was crushed concrete, concrete surface longitudinal cracks; convex side of the pressure suddenly changed from tension, transverse cracks appear; destruction before the horizontal deflection increased rapidly rather sudden destruction come, leading to instability Damage. Carrying capacity is less than the same cross section, reinforcement, material columns. § 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member

S 6.1 with a longitudinal axis of the stirrup steel bar and the JPKIC general compression member 结构热计原黑 3.Longitudinal stability factor 1)Definition:slenderness ratio of members to consider the additional effect of increasing the calculation of bearing capacity reduction factor. 2)Calculation:=ps (6-1) p=zEl 6N (Euler's formula Damage to the critical long column capacity P =fcA+(Columns axis force at failure π2BE。.1 0= fed+fap 3)influencing factors:the slenderness ratio,column initial deflection,the eccentric vertical force is related to concrete strength,steel reinforcement ratio of their intensity level and less affected

3.Longitudinal stability factor 1) Definition: slenderness ratio of members to consider the additional effect of increasing the calculation of bearing capacity reduction factor. 2) Calculation: =pl/ps (6-1) (6-2) 3) influencing factors: the slenderness ratio, column initial deflection, the eccentric vertical force is related to concrete strength, steel reinforcement ratio of their intensity level and less affected. (Columns axis force at failure (Euler' sformula Damage to the critical long column capacity 2 0 2 s s s l p fcA f A l EI p = +   = ）  2 1 ' ' 2 c 1 cd sd E f f      =  + § 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member

JPKIC 结构设计原理 Theprimepletstricturedesio S 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member 4.Calculation of bearing capacity ,provides the force with a longitudinal axis of the stirrup steel bar and the general cross-section bearing capacity of compression members is calculated as ≤YoNa N=0.9ofaA+faA） Column ordinary hoops Calculation of bearing capacity and strength of sub-section design review two cases. 1)section design Given section size,length 10,axial compressive strength of concrete and steel design value of compressive strength,axial pressure combined design value,find the required area of longitudinal reinforcement. 2)Review Section Given section size,length 10,all cross-sectional area of longitudinal reinforcement,the axial compressive strength of concrete and steel design value of compressive strength,mix design value of axial force,find the section bearing capacity

4.Calculation of bearing capacity 《Highway Bridge Specifications》, provides the force with a longitudinal axis of the stirrup steel bar and the general cross-section bearing capacity of compression members is calculated as ≤ (6-3) Column ordinary hoops Calculation of bearing capacity and strength of sub-section design review two cases. 1) section design Given section size, length l0, axial compressive strength of concrete and steel design value of compressive strength, axial pressure combined design value, find the required area of ​longitudinal reinforcement. 2) Review Section Given section size, length l0, all cross-sectional area of ​longitudinal reinforcement, the axial compressive strength of concrete and steel design value of compressive strength, mix design value of axial force, find the section bearing capacity. 0 Nd  ( ) ' ' 0.9 u cd s d As N =  f A + f § 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member

JPKic 结构设计原理 The principle of structure design 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member 5.Construction requirements 1)concrete Generally use more C25~C40 grade concrete. 2)Section size/b30 ②≥25×25cm ③modulus size: 25,30,35...,not less than 250mm. 3)Longitudinal reinforcement Diameter:12 ~32cm,root for the >4,clear distance between longitudinal reinforcement 5cm,the net protective layer:>2.5cm

5.Construction requirements 1) concrete Generally use more C25～C40 grade concrete. 2) Section size ① ② ③ modulus size: 25,30,35 ..., not less than 250mm. 3) Longitudinal reinforcement Diameter: 12 ~ 32cm, root for the ≥ 4, clear distance between longitudinal reinforcement ≥ 5cm, the net protective layer: ≥ 2.5cm l o / b  30  25  25cm § 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member

JPKIC 结构设计原理 s6.1 with a longitudinal axis of the stirrup steel bar and then general compression member 4)stirrups hoop diameter:not less than the longitudinal bar diameter of 1/4,and not less than 8mm; the spacing:should not exceed 15 times the diameter of longitudinal reinforcement,and not larger than the smaller member section size(diameter of circular section with a 0.8-fold),not greater than 400mm;in longitudinal cross- sectional area of more than reinforced concrete calculation Cross-sectional area of 3%,the stirrup spacing shall be not more than 10 times the diameter of longitudinal reinforcement,and not a large 200mm. Ocomposite hoop:hoop set up along the vertical spacing of reinforcement bars from the corner or 15 times greater than the diameter of the stirrup 150mm (whichever is greater)range,you should set the composite stirrups

4) stirrups ● hoop diameter: not less than the longitudinal bar diameter of 1 / 4, and not less than 8mm; ● the spacing: should not exceed 15 times the diameter of longitudinal reinforcement, and not larger than the smaller member section size (diameter of circular section with a 0.8-fold), not greater than 400mm; in longitudinal cross￾sectional area of ​more than reinforced concrete calculation Cross-sectional area of 3%, the stirrup spacing shall be not more than 10 times the diameter of longitudinal reinforcement, and not a large 200mm. ● composite hoop: hoop set up along the vertical spacing of reinforcement bars from the corner or 15 times greater than the diameter of the stirrup 150mm (whichever is greater) range, you should set the composite stirrups. § 6.1 with a longitudinal axis of the stirrup steel bar and the general compression member

JPKic 箱构試原黑 6.2 with a longitudinal axis of bar and spiral hoop compression member 1.Stress analysis and failure 1)Stress Analysis Ring spiral stirrups stirrups or welded to the axial stress of confined concrete under the lateral deformation produced on the concrete indirect passive lateral pressure,thereby enhancing the compressive strength and deformation capacity. Central to the tension hoop is generated.When the external stirrups and spalling of concrete is crushed,the stirrups of the concrete within the core could continue to bear the load,when the tensile yield strength of stirrups to the loss of lateral deformation of concrete capacity constraints, the core concrete will Caused by crushing the whole component damage, the failure mode as shown in Figure 6-2

§ 6.2 with a longitudinal axis of bar and spiral hoop compression member 1.Stress analysis and failure 1) Stress Analysis Ring spiral stirrups stirrups or welded to the axial stress of confined concrete under the lateral deformation produced on the concrete indirect passive lateral pressure, thereby enhancing the compressive strength and deformation capacity. Central to the tension hoop is generated. When the external stirrups and spalling of concrete is crushed, the stirrups of the concrete within the core could continue to bear the load, when the tensile yield strength of stirrups to the loss of lateral deformation of concrete capacity constraints, the core concrete will Caused by crushing the whole component damage, the failure mode as shown in Figure 6-2