The behaviour of granular material in pure shear, direct shear and simple shear

In biaxial compression tests, the stress calculations based on boundary information underestimate the principal stresses leading to a significant overestimation of the shear strength. In direct shear tests, the shear strain becomes highly concentrated in the mid-plane of the sample during the test. Although the stress distribution within the specimen is heterogeneous, the evolution of the stress ratio inside the shear band is similar to that inferred from the boundary force calculations. It is also demonstrated that the dilatancy in the shear band significantly exceeds that implied from the boundary displacements. In simple shear tests, the stresses acting on the wall boundaries do not reflect the internal state of stress but merely provide information about the average mobilised wall friction. It is demonstrated that the results are sensitive to the initial stress state defined by K0 = sh/sv. For all cases, non-coaxiality of the principal stress and strain-rate directions is examined and the corresponding flow rule is identified. Periodic cell simulations have been used to examine biaxial compression for a wide range of initial packing densities. Both constant volume and constant mean stress tests have been simulated. The characteristic behaviour at both the macroscopic and microscopic scales is determined by whether or not the system percolates (enduring connectivity is established in all directions). The transition from non-percolating to percolating systems is characterised by transitional behaviour of internal variables and corresponds to an elastic percolation threshold, which correlates well with the establishment of a mechanical coordination number of ca. 3.0. Strong correlations are found between macroscopic and internal variables at the critical state.

Constant shear along a boundary of a flume

'I'he accurate rreasurement of bed shear stress has been extremely difficult due to its changing values until white propunded a theory which would give constant shear along the bed of a flume. In this investigation a flume has been designed according to White's theory and by two separate methods proven to give constant shearing force along the bed. The first method applied the Hydrogen Bubble Technique to obtain accurate values of velocity thus allowing the velocity profile to be plotted and the momentum at the various test sections to be calculated. The use of a 16 mm Beaulieu movie camera allowed the exact velocity profiles created by the hydrogen bubbles to be recorded whilst an analysing projector gave the means of calculating the exact velocities at the various test sections. Simultaneously Preston's technique of measuring skin friction using Pitot tubes was applied. Twc banks of open ended water manometer were used for recording the static and velocity head pressure drop along the flume. This tvpe of manometer eliminated air locks in the tubes and was found to be sufficiently accurate. Readings of pressure and velocity were taken for various types and diameters of bed material both natural sands and glass spheres and the results tabulated. Graphs of particle Reynolds Number against bed shear stress were plotted and gave a linear relationship which dropped off at high values of Reynolds number. It was found that bed movement occurred instantaneously along the bed of the flume once critical velocity had been reached. On completion of this test a roof curve inappropriate to the bed material was used and then the test repeated. The bed shearing stress was now no longer constant and yet bed movement started instantaneously along the bed of the flume, showing that there are more parameters than critical shear stress to bed movement. It is concluded from the two separate methods applied that the bed shear stress is constant along the bed of the flume.

Concrete beams with stirrups subject to torsion, shear and bending

This thesis examines experimentally and theoretically the behaviour and ultimate strength of rectangular reinforced concrete members under combined torsion, shear and bending. The experimental investigation consists of the test results of 38 longitudinally and transversely reinforced concrete beams subjected to combined loads, ten beams of which were tested under pure torsion and self-weight. The behaviour of each test beam from application of the first increment of load until failure is presented. The effects of concrete strength, spacing of the stirrups, the amount of longitudinal steel and the breadth of the section on the ultimate torsional capacity are investigated. Based on the skew-bending mechanism, compatibility, and linear stress-strain relationship for the concrete and the steel, simple rational equations are derived for the three principal modes of failure for the following four types of failure observed in the tests: TYPE I Yielding the reinforcement, at failure, before crushing the concrete. TYPE II Yielding of the web steel only, at failure, before crushing the concrete. TYPE III Yielding of the longitudinal steel only, at failure, before crushing the concrete. TYPE IV Crushing of the concrete, at failure, before yielding of any of the reinforcement.

Prestressed concrete beams with stirrups subjected to torsion, bending and shear

Reported in this thesis are test results of 37 eccentrically prestressed beams with stirrups. Single variable parameters were investigated including the prestressing force, the prestressing steel area, the concrete strength, the aspect ratio h/b and the stirrups size and spacing. Interaction of bending, torsion and shear was also investigated by testing a series of beams subjected to varying bending/torsional moment ratios. For the torsional strength an empirical expression of linear format is proposed and can be rearranged in a non-dimensional interaction form: T/To+V/Vo+M/Mo+Ps/Po+Fs/Fo=Pc2/Fsp. This formula which is based on an average experimental steel stress lower than the yield point is compared with 243 prestressed beams containing ' stirrups, including the author's test beams, and good agreement is obtained. For the theoretical analysis of the problem of torsion combined with bending and shear in concrete beams with stirrups, the method of torque-friction is proposed and developed using an average steel stress. A general linear interaction equation for combined torsion with bending and/or shear is proposed in the following format: (fi) T/Tu=1 where (fi) is a combined loading factor to modify the pure ultimate strength for differing cases of torsion with bending and/or shear. From the analysis of 282 reinforced and prestressed concrete beams containing stirrups, including the present investigation, good agreement is obtained between the method and the test results. It is concluded that the proposed method provides a rational and simple basis for predicting the ultimate torisional strength and may also be developed for design purposes.

Serrated yielding and the localized shear failure mode in aluminium alloys

A study has been made of serrated yielding in two commercial Al-Zn-Mg alloys in the as-quenched condition. The different serration types produced in the two alloys and the shear failure mechanism observed in both notched-bend and tensile testing are related to the mechanisms of dynamic strain ageing occurring during the test. An estimate of 19.7 kJ/mole for the activation energy for exchange of a solute atom and a vacancy in Al-6.2 wt% Zn, 2.5 wt% Mg has been made. © 1981.