Advanced Theory of Concrete Structures Chapter 4 Bending and Compression Behavior of RC Structural Members Yong Zhou College of Civil Engineering,Tongji University 土本工程学院 yongzhou@tongji.edu.cn COLLEGEOPCVILINGAINETRING
Yong Zhou College of Civil Engineering, Tongji University yongzhou@tongji.edu.cn Chapter 4 Bending and Compression Behavior of RC Structural Members Advanced Theory of Concrete Structures
4.1 Bending behavior of concrete structural members
4.1 Bending behavior of concrete structural members
Engineering applications slab stairs column Rotaining Bridge foundation all eam Deck beam 1ZZ1WA/1VWK布 wall footing spread footing
Engineering applications Retaining Wall Bridge Deck spread footing slab column beam foundationwall beam stairs wall footing 3
Experimental Study b M Crushing of conerete Ⅲ Yielding of rebar LVDT M M C Cracking of concrete 0 ■迹
4 F F Strain gauge LVDT M V h a b As h 0 xn e c es Experimental Study C Ⅰ Ⅱ Ⅲ M cr M y M u 0 δ, φ P, M y Yielding of rebar Crushing of concrete Cracking of concrete
Failure Modes (a) over-reinforced under-reinforced b) 0= As() bho steel content 目土本工程学院
5 over-reinforced under-reinforced few steel content Mu 0 f M My C ρ>ρb B ρmin<ρ<ρb A ρ<ρmin (%) bh0 As = Failure Modes 5
Flexure strength vs.steel ratio Strain profiles ☑☑ Steel 10 09 00 egion B-C: 0 0A- 000m 土本又程学院 T特N力N时门度事 6
6 Flexure strength vs. steel ratio 6
Basic Assumptions l.“Plane sections remain plane'”assumption A 8 dy Snho ho (1-5n)ho ●● 6 6 nho y ho-as' (1-5m)h 目土本工程学汽
7 7 0 0 0 ' (1 ) ' h y h a n h s n s c s n t c e e e e f − = − = = = as As e c t b h As ’ as ’ y dy et b es es ’ e c f nh0 (1- n )h0 h0 1. “Plane sections remain plane” assumption Basic Assumptions
191 0.004 Column B-3a Column A-15b e=5.0in 0.002 e=12.5in Yield 75 kips =4850 psi point 卷r:0.003 =125.9 kips 125 kips =79.0 kips 60 0.001 40 0.002 90 20 0 0.001 60 ( 30 0.001 Yield 0.001 0.002 Yield point> Column B.2a 0.002 210 kip Column A-20b e=2.5 in f6=4250ps1 e=15.0 in =213 kips =5000ps1 0.001 180 ma-63.5 kips 0 120 60 0.001 Yield point 土本工程学院 特 8
8 8
Basic Assumptions 2.Tensile strength of concrete is neglected in calculation of flexural strength. d M Soho (1-5n)ho 6 3.The strain in the reinforcement is equal to the strain in the concrete at the same level. 目土本工程学院 9
9 9 2. Tensile strength of concrete is neglected in calculation of flexural strength. M T xc Tc C 3. The strain in the reinforcement is equal to the strain in the concrete at the same level. e c t et b es es ’ e c f nh0 (1- n )h0 Basic Assumptions
Basic Assumptions 4.Constitutive laws f o。=f1-(1-6)] 0 o。=fc 80≤8≤Em 0 O=E,88≤8y 0=f)8>6,y o,=E,6 土水工程学院 得 10
10 10 4. Constitutive laws c c cu n c c f f e e e e e e e = = − − 0 0 0 [1 (1 ) ] σ ε0 εu fc y y s y f E e e e e e = = s es s=Eses e y esu fy Basic Assumptions
