TORSION IN BEAMS

Investigation of Torsion in Beams Made From High Strength Concrete

ABSTRACT

The rapid advancement in concrete technology allows the use of high strength concrete on a commercial level and since it is an ideal material for structural members predominantly loaded in compression and also for those spanning long distances, such as bridge decks. Some of the main advantages of using high strength concrete in bridge decks are due to economical gain in smaller and durable member section. However these are offset by early cover spilling and poor ductility.

Design for torsion unlike design for bending and shear, which have been perfected over the years, has not attracted as much attention and is in a rather weaker state. Despite the latest developments in concrete technology which has produced concrete with high strength, torsional shear stresses are still fixed at historic levels. Dealing with torsion in today's codes of practice is very primitive and does not consider the improved properties of High Strength Concrete. Predictions of current standards for the ultimate torsional capacity of reinforced concrete beams are found to be too conservative especially in beams made from High Strength Concrete.

This project provides preliminary results from an investigation that is aimed at illustrating the influence of concrete strength on the torsional behaviour of reinforced concrete beams. The objective of this project is to investigate the reasons why design codes are still limiting torsional shear stresses at historic levels despite the recent development in concrete technology. The overall study is aimed at identifying the economic advantages that could be gained from allowing high values of torsion to be used in future design codes and to investigate the reasons why design codes incorporate this limitation. This research project proposes an extension of the EC2 Design Codes to cover torsional strength of High Strength Concrete. The basic approach will consists of determining the concrete contribution to the ultimate strength of a member and then proportioning reinforcement for the remaining portion of the required ultimate strength.

Notation

a maximum aggregate size

b beam width

bf width of compression flange

C cohesion

d effective depth

EC2 Eurocode 2

FOS factor of safety (FOS for shear ¼ Vdesign divided by

overall load factor)

f 9c concrete cylinder strength

fcu concrete cube strength

fy yield strength of reinforcement (subscript

k ¼ characteristic value)

hf depth of compression flange

Pcr load at which first cracks originated

Pult ultimate failure load

SI stirrup index SI ¼ rw f y=(v f 9c)

s stirrup spacing

V shear force

Vc concrete component of shear resistance

Vcz shear carried by the compression zone

Vdesign design ultimate shear resistance divided by overall load

factor

VRdc EC2 design shear resistance for beams without shear

reinforcement

Vs stirrup contribution to shear resistance

VSI EC2 variable strut inclination design method

z lever arm for shear (0.9d unless noted otherwise)

ac, as partial factors for concrete and steel respectively

L inclination of compressive stress field to the

longitudinal axis of the beam_ coefficent of friction along crack plane

_ strength reduction factor for concrete cracked in shear

v ¼ 0:6(1 _ f 9c=250)

rl longitudinal reinforcement ratio rl ¼ Asl/(bd)

rw shear reinforcement ratio rw ¼ Asw/(bs)

_n normal stress to crack plane

_ shear ...