Chapter 6: Continuous composite Beams 连续组合梁 By Prof.Chen Shiming Lecture Notes for Presentation 2013
By Prof. Chen Shiming Lecture Notes for Presentation 2013 Chapter 6: Continuous composite Beams 连续组合梁
Objective/Scope To describe the behaviour of continuous composite beams(连续组合梁受力和承载 特性)方 ·Rigid-plastic analysis(塑性极限方法) To determine internal moments and forces, and to evaluate moment redistribution. ·连续组合梁的内力分析，重分布
Objective/Scope • To describe the behaviour of continuous composite beams (连续组合梁受力和承载 特性); • Rigid-plastic analysis(塑性极限方法) • To determine internal moments and forces, and to evaluate moment redistribution. • 连续组合梁的内力分析,重分布
6.1 Introduction Advantages of continuous beams:(特征、优点) .1)greater load capacity due to redistribution of moments;ii)greater stiffness Disadvantages associated with continuous beams: i)increased complexity in design ii)susceptibility to buckling in the negative moment region(局部屈曲，侧扭失稳 ) Design/detailed calculations or global analysis': to determine internal moments and forces in critical regions for the various loading cases and limit states 极限状态的内力分析
6.1 Introduction Advantages of continuous beams : (特征、优点) • i) greater load capacity due to redistribution of moments; ii) greater stiffness • Disadvantages associated with continuous beams: i) increased complexity in design ii) susceptibility to buckling in the negative moment region （局部屈曲，侧扭失稳） • Design/ detailed calculations or ‘global analysis’ : to determine internal moments and forces in critical regions for the various loading cases and limit states 极限状态的内力分析
The salient(turn)point in regard to serviceability and strength needs to take into account that composite beams in hogging bending behave completely differently than beams subjected to sagging bending. In hogging bending the concrete slab is subjected to tension,and this will significantly affect both the stiffness and strength of the cross sections in hogging moment regions
• The salient (turn) point in regard to serviceability and strength needs to take into account that composite beams in hogging bending behave completely differently than beams subjected to sagging bending. • In hogging bending the concrete slab is subjected to tension, and this will significantly affect both the stiffness and strength of the cross sections in hogging moment regions
The concrete in the mid Cracked concrete Reinforcement span region is in compression and the steel in tension Hogging Over the internal support this distribution reverses. The concrete cannot carry Sagging Bending moment diagram significant tensile strains and therefore cracks,the embedded reinforcement as effective in resisting Section X-X Section Y-Y moment.(混凝土开裂，钢 梁易屈曲、失稳) Strain Stress Strain stress
The concrete in the mid span region is in compression and the steel in tension. Over the internal support this distribution reverses. The concrete cannot carry significant tensile strains and therefore cracks, the embedded reinforcement as effective in resisting moment.（混凝土开裂，钢 梁易屈曲、失稳）
Local buckling 局部屈曲 Distosional lateral buckling 组合梁侧扭失稳
Distosional lateral buckling 组合梁侧扭失稳 Local buckling 局部屈曲
Steel reinforcement ·Internal moments in continuous composite beams can be determined by elastic analysis or, -Structural steel subject to certain section conditions,by rigid-plastic analysis 结构分析方法：弹性分析， 塑性极限分析 Negative moment Whether plastic analysis is (a)Both spans loaded appropriate depends on the susceptibility of the beam to local buckling: 0 塑性极限分析适用条件 Negative moment
• Internal moments in continuous composite beams can be determined by elastic analysis or, subject to certain conditions, by rigid-plastic analysis. • 结构分析方法：弹性分析， 塑性极限分析 • Whether plastic analysis is appropriate depends on the susceptibility of the beam to local buckling： • 塑性极限分析适用条件
Tension in slab Applied moment reinforcement Shear in connector (opposite to sagging) Tension or compression in bolts internal Compression in moments in Stiffener bottom flange beam column Vertical shear connection in bolts Forces on the beam column connection in a continuous composite beam However there is also the transfer of longitudinal shear between the concrete and steel to consider and the fact that the bottom part of the steel section is in compression and therefore both flange and web are prone to buckling
internal moments in beam column connection
Point of contraflexure Bending moment diagram Support column Side view Section A-A Displacement V along beam Plan view of bottom flange showing buckle wavelength Maximum buckle length in continuous beam
6.2 Cross Section Classification In a continuous beam,the critical cross-sections must be capable of developing/sustaining their plastic resistance moment,under increasing load, sufficient regions have fully-yield for a mechanism of plastic hinges to be present.(plastic design) The mechanism arises as a result of redistribution of moment.To ensure that the resulting strains can be accommodated without a reduction in resistance below the plastic moment,limitations must be placed on the slenderness of the elements of the cross-section which are in compression
6.2 Cross Section Classification • In a continuous beam, the critical cross-sections must be capable of developing/sustaining their plastic resistance moment, under increasing load, sufficient regions have fully-yield for a mechanism of plastic hinges to be present. (plastic design) • The mechanism arises as a result of redistribution of moment. To ensure that the resulting strains can be accommodated without a reduction in resistance below the plastic moment, limitations must be placed on the slenderness of the elements of the cross-section which are in compression