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Abstract
Nine asymmetrically spanned reinforced concrete deep beams were designed and tested to unreinforced web crushing failure in this experimental study to establish the appropriate shear stress limit for beam design. The lower bound and mean shear design limits associated with the concrete strut crushing in the web of the beam are identified, based on the better correlated concrete compressive strength parameter rather than its square root. A unified shear stress limit model is proposed to anchor the maximum strut crushing limit and sectional shear stress in design codes via a generic shear enhancement factor. The proposed unified model exhibits modest conservatism compared to the Hong Kong Code of Practice for Structural Concrete 2013 and the Chinese Code for Design of Concrete Structures (GB 50010). Transfer beams, pile caps and corbels, which are typically accompanied by high shear demand, can be optimised in size to leverage construction material cost savings through the more relaxed shear stress limit proposed in this study, which is justified through experiments.
Notations
| a | = | shear span between centreline of the load and support |
| b | = | beam width |
| d | = | beam effective depth |
| dshear | = | beam depth for shear calculation, assumed as 0.8D |
| fc′ | = | compressive cylinder strength of concrete |
| fcu | = | compressive cube strength of concrete |
| fstruct CCC | = | strut stress adjacent to CCC node in the STM |
| ftk | = | characteristic tensile strength of concrete |
| fy | = | yield strength of steel reinforcement |
| fu | = | tensile strength of steel reinforcement |
| hLong | = | longitudinal bar height from soffit to centre of top layer bar |
| vc | = | shear stress capacity of concrete |
| vc strut | = | proposed shear stress capacity of concrete corresponding to the STM strut |
| vc code | = | codified shear stress capacity of concrete |
| w | = | narrower strut width, in this case taken as the width adjacent to the CCC node |
| z | = | bending moment lever arm |
| As | = | steel reinforcement cross-section area |
| Aeff | = | effective shear cross-section area of concrete |
| D | = | beam total depth |
| E | = | Young's modulus |
| Hstirrups | = | horizontal stirrups |
| L | = | beam length |
| L′ | = | clear span |
| P | = | applied point load |
| V | = | shear force |
| Vstirrups | = | vertical stirrups |
| β | = | strut efficiency factor |
| γshear | = | material partial safety factor for shear load |
| ρ | = | longitudinal reinforcement ratio |
| θ | = | strut angle with respect to horizontal tie |
Additional information
Funding
Notes on contributors
Daniel T W Looi
Mr Daniel T W Looi obtained his B.Sc. Eng. (Hons) degree from University of Malaya, Kuala Lumpur, Malaysia. He is currently a Postgraduate Candidate under the supervision of Associate Professor, Ir Dr Ray Su in the Department of Civil Engineering at The University of Hong Kong. He worked as a Structural Engineer in both the high-rise building and plant industry for five years. He is a member of the Malaysia EC8 earthquake code annex drafting committee. His research interests include shear strength and the seismic design of concrete buildings in low-to-moderate seismicity regions.
Ray K L Su
Ir Dr Ray K L Su is an Associate Professor of Structural Engineering, the Department of Civil Engineering at The University of Hong Kong. He obtained his B.Sc. (Eng) and Ph.D. degrees from the University of Hong Kong. His current research interests lie in the development of new theories suitable for the seismic assessment and design of concrete and masonry structures, strengthening concrete members using external steel plates and the evaluation of the fracture properties of concrete and graphite. He is currently serving as the Secretary of Structural Discipline in the Hong Kong Institution of Engineers (HKIE) and acts as the Principal Investigator for some consultancy and research projects related to strengthening of concrete structures and seismic design of buildings.
Eddie S S Lam
Ir Dr Eddie S S Lam is an Associate Professor of Structural Engineering, the Department of Civil and Environmental Engineering at The Hong Kong Polytechnic University and has had a varied career in civil, structural and mechanical engineering. He received his Ph.D. degree in 1989 from the University of Southampton, the UK. His current interest is in the strengthening of concrete structures. He is a former Chairman of the HKIE Structural Division, a member of the HKIE Structural Discipline and a Council Member of the Institution of Structural Engineers (IStructE).