Shear Capacity Prediction for RC Beams Without Stirrups Based on Mechanical Research

doi:10.12141/j.issn.1000-565X.210217

Abstract

Abstract:

Starting from the critical failure inclined section of reinforced concrete beam without stirrups, this study analyzed the force of each part on the critical failure inclined section. Through theoretical derivation and rational simplification, the value of calculation parameters was obtained, and the calculation model of shear capacity of based on mechanical balance for the reinforced concrete beam without stirrups. On the basis of the classical mechanics principle, the model has a clear physical meaning and can better reflect the influences of shear parameters including concrete strength, shear-span ratio, longitudinal reinforcement ratio and size effect, respectively. Then, the prediction accuracy and stability of the proposed shear model were evaluated based on 9 test specimens by comparing with the GB 50010—2010, ACI 318-14, EC 2, JSCE 2007 and Zsutty calculation formula. Finally, the applicability of the proposed model in the calculation of shear capacity of FRP reinforced concrete beams without stirrups was verified. The results show that the proposed model based on mechanical balance can effectively predict the shear capacity of reinforced concrete beams without stirrups and exhibit the shear failure mechanism of beam oblique section. Moreover, the proposed shear model has a higher prediction accuracy and stability, and can better reflect the nonlinear relationship between shear capacity versus shear-span ratio and longitudinal reinforcement ratio. In addition, the predicted results have a consistent stability with the change of shear parameters, so it can be applied to the shear capacity calculation of FRP reinforced concrete beams without stirrups.

Key words: reinforced concrete beam without stirrups, mechanical analysis, shear test, shear bearing capacity, prediction accuracy

CLC Number:

TU375.1

XIONG Ergang, ZU Kun, HU Qinbin, et al. Shear Capacity Prediction for RC Beams Without Stirrups Based on Mechanical Research[J]. Journal of South China University of Technology(Natural Science Edition), 2022, 50(11): 115-124.

Figures/Tables 16

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Calculation models for the shear capacity of RC beams without stirrups"

计算模型	计算公式	参数备注
中国规范 GB 50010—2010^［18］	$V c = α c v β h f t b h 0$	α_cv为构件斜截面受剪承载力系数；β_h为截面高度影响系数；f_t为混凝土轴心抗拉强度设计值；b为矩形截面的宽度或T形、I形截面腹板的宽度；h₀为截面有效高度
美国规范 ACI 318-14^［16］	$V c = (0.158 f c' + 17.2 ρ w V u d M u) b w d ≤ 0.291 f c' b w d$ 简化式 $V c = 0.17 λ f c' b w d$	f_c'为混凝土圆柱体抗压强度值；ρ_w为纵筋配筋率；V_u、M_u分别为计算截面的剪力和弯矩值；b_w为截面腹板宽度；d为截面有效高度
欧洲规范 EC 2^［19］	$V R d, c = C R d, c k (100 ρ l f c k) 1 / 3 b w d$ $V R d, c ≥ 0.035 k 3 / 2 f c k 1 / 2 b w d$ $C R d, c = 0.18 / γ c$ $k = 1 + 200 / d ≤ 2.0$	C_Rd，c为材料修正系数，其中γ_c为混凝土材料分项系数，持久设计状态下取1.5，偶然设计情况时取1.2；k为尺寸效应影响系数，f_ck为混凝土圆柱体抗压强度特征值；ρ₁为纵向受拉钢筋配筋率，ρ₁≤2.0%；当剪跨长度为0.5d≤a<2d时，将结果除以系数β=a/2d；当a<0.5d时，取a=0.5d；其他参数同美国ACI 318-14规范
日本规范 JSCE 2007^［20］	$V c d = β d β p β n f v c d b w d γ b$ ； $β n = 1 + M 0 / M d ≤ 2.0, ????? N d' ≥ 0 ? 1 + 2 M 0 / M d ≥ 0, ????? N d' < 0$ $β d = 1 ? 000 / d 1 / 4 ≤ 1.50$ $β p = 100 ρ v 1 / 3 ≤ 1.50$	β_d为尺寸效应计算系数；ρ_v为纵筋配筋率；β_n为考虑弯曲应力和轴力作用系数；N_d'为轴向压力设计值；M₀为设计弯矩值；M_d为轴向力引起的弯矩；γ_b为承载力分项系数，取1.3
Zsutty公式^［21］	$V c = 2.2 (f c' ρ d a) 1 / 3 b d, ????????????? a d ≥ 2.5 (2.5 d a) 2.2 (f c' ρ d a) 1 / 3 b d, ?????? a d < 2.5$	参数同美国ACI 318-14规范
中国规范 GB 50608—2010^［22］	$V c = 0.86 f t b w c$ ； $c = k h o f$ $ρ f = A f / b w h o f$ $k = 2 ρ f α f + (ρ f α f) 2 - ρ f α f$	c为截面中和轴到受压区边缘的距离；A_f 为纵向受拉FRP筋截面面积；ρ_f 为纵向受拉FRP筋配筋率；α_f 为FRP筋与混凝土弹性模量之比；h₀_f 为纵向受拉FRP筋合力点至截面受压区边缘的距离
美国规范 ACI 440.1R-15^［23］	$V c = 5 f c' b w (k d)$	参数同我国GB 50608—2010规范
加拿大规范 CSA S806-12^［24］	$V c = 0.05 λ ? c k m k r f c' 3 b w d$ $k m = V f d M f ≤ 1$ ； $k r = 1 + E F ρ F W 3$	λ为混凝土密度折减系数，对普通混凝土取1；?_c为混凝土抗力系数，取值为0.65；E_F为FRP筋的弹性模量；ρ_FW为FRP纵筋的配筋率；当d≥300 mm时，在计算中引入尺寸效应因子k_s来考虑尺寸效应的影响，其中k_s=750/（450+d）≤1.0

Table 5

Table 6

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Fig.9

Table 7

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试件编号	λ	a /mm	d /mm	A_s /mm²	ρ /%
R1-1.13-700	3.21	700	218	307.88	1.13
R2-1.42-700	3.21	700	218	386.42	1.42
R3-1.85-700	3.48	700	201	464.96	1.85
R4-1.13-575	2.64	575	218	307.88	1.13
R5-1.42-575	2.64	575	218	386.42	1.42
R6-1.85-575	2.86	575	201	464.96	1.85
R7-1.13-400	1.83	400	218	307.88	1.13
R8-1.42-400	1.83	400	218	386.42	1.42
R9-1.85-400	1.99	400	201	464.96	1.85

直径/mm	强度等级	f_y/ MPa	f_u /MPa	E_s /GPa	屈服应变/10^-3
6.5	HPB 300	411	575	197.65	2.08
10	HRB 400	447	594	203.65	2.19
14	HRB 400	439	591	198.27	2.21

试件	P_cr /kN	P_u /kN	υ_u /MPa
R1-1.13-700	11	62.53	2.29
R2-1.42-700	14	82.02	3.01
R3-1.85-700	15	80.43	3.20
R4-1.13-575	21	84.53	3.10
R5-1.42-575	20	85.81	3.15
R6-1.85-575	22	90.02	3.58
R7-1.13-400	23	108.25	3.97
R8-1.42-400	24	164.44	6.03
R9-1.85-400	26	136.80	5.44

试件编号	V_test/kN	V_MEC/kN	V_GB/kN	V_ACI/kN	V_{EC 2}/kN	V_JSCE/kN	V_Zsutty/kN	V_pre/V_test
试件编号	V_test/kN	V_MEC/kN	V_GB/kN	V_ACI/kN	V_{EC 2}/kN	V_JSCE/kN	V_Zsutty/kN	MEC	GB	ACI	EC 2	JSCE	Zsutty
R1-1.13-700	31.27	27.28	24.37	22.51	19.36	18.55	26.47	0.87	0.78	0.72	0.62	0.59	0.85
R2-1.42-700	41.01	36.85	24.37	22.51	20.89	20.02	28.57	0.90	0.59	0.55	0.51	0.49	0.70
R3-1.85-700	40.22	38.59	22.47	20.76	21.46	20.57	28.00	0.96	0.56	0.52	0.53	0.51	0.70
R4-1.13-575	42.27	38.91	26.78	22.51	19.36	18.55	28.27	0.92	0.63	0.53	0.46	0.44	0.67
R5-1.42-575	42.91	42.85	26.78	22.51	20.89	20.02	30.50	1.00	0.62	0.52	0.49	0.47	0.71
R6-1.85-575	45.01	39.94	23.29	20.76	21.46	20.57	29.90	0.89	0.52	0.46	0.48	0.46	0.66
R7-1.13-400	54.13	58.94	34.45	22.51	19.36	18.55	43.47	1.09	0.64	0.42	0.36	0.34	0.80
R8-1.42-400	82.22	82.09	34.45	22.51	20.89	20.02	46.91	1.00	0.42	0.27	0.25	0.24	0.57
R9-1.85-400	68.40	77.31	30.06	20.76	21.46	20.57	42.39	1.13	0.44	0.30	0.31	0.30	0.62
平均值								0.97	0.58	0.48	0.45	0.43	0.70
变异系数								0.09	0.18	0.27	0.24	0.24	0.11

统计指标	规范及模型
统计指标	文中计算模型	GB 50608— 2010	ACI 440.1 R-15	CSA S806-12
Mean	1.03	0.34	0.53	0.57
COV	0.18	0.39	0.31	0.19
Min	0.18	0.04	0.06	0.07
Max	2.13	0.75	0.91	0.86
ξ_0.05	0.62	0.1	0.17	0.4
ξ_0.95	1.58	0.54	0.75	0.76