FURTHER NOTES ON A STEEL ENERGY-ABSORBING ELEMENT FOR BRACED FRAMEWORKS

The paper gives working loads and deflections for braced frameworks in which rectangular energy absorbing elements fabricated from round steel bar are incorporated to ensure reliable performance during earthquake attack. In a practical design example the locking up forces which occur for gross deformations of the system are calculated.


INTRODUCTION 2. 2 Tests at PEL, DSIR
The publication of the paper in the Bulletin (1) describing tests on an energy absorbing element fabricated from round steel bar and incorporated in the bracings of a framework ( Fig. 1) has resulted in increased use of this type of energy absorber in structures, in particular in pole houses and small buildings.
This has prompted enquiries into aspects not specifically covered in the original paper, one of which is the deflection obtained at first yield of the absorber.
It will be recalled that the advantage of the system is that the progressive slack which normally develops in the bracings of a framed structure under earthquake overload does not occur when this type of element is fitted. Essentially for a rectangular frame, the inner energy absorbing frame has the same proportions as the outer framework, i.e. the line of the diagonals are coincidental.

2.
CHARACTERISTICS OF DEVICES ALREADY TESTED 2.1 Tests by Smith and Henry (2) The first tests were carried out by consulting engineers Smith and Henry in Auckland in 1978 on the frame shown in Fig. 2, for a slowly applied increasing load across one diagonal.
Two 24 mm diameter bars were employed in the energy absorbing element, loaded by single 24 mm diameter bars in the main frame.
The graph of load against deflection shown in Fig. 3 was obtained.
As would be expected there was a gradual departure from the straight-line characteristic from the time yield first developed on the outer limits of the sections in bending, which were located just outside the fittings transmitting the load to the corners of the rectangle.
First departure from linearity is noticed at a load of about 13 kN. * Physics and Engineering Laboratory, DSIR, Gracefield, Lower Hutt.
In the tests at PEL on a square frame ( Fig. 1), fabricated from 25 mm bars, no specific attempt was made to obtain a value for the load at first yield for a slowly applied static load.
The results obtained were for cyclic testing only at 1 Hz. Fig. 4 shows a typical set of loops obtained during the course of testing. Indications are that first yield occurred at the limits of the first narrow loop, i.e. at a load of about 5 kN.
The width of this loop was probably dictated by friction effects at the pins in the rig and on the pads on which the frame rested.

3.
THEORETICAL LOAD AND DEFLECTION CHARACTERISTICS FOR ROUND-BAR ABSORBERS

.1 Yield Condition
For an absorber loaded across a diagonal shown in Fig. 5

Effective Length of Sides of Absorber
Preliminary calculations suggest that, to allow for the rigidity of the corner fittings at the load points, and the consequent yield of the bars outside the width of the fittings, effective lengths I' and h 1 , which are less than I and h respectively, should be taken in calculation work in order to obtain meaningful estimates of the shear capacity of the absorber.
In the following calculations 1 1 and h' have been taken as the lengths between the intersection of the centre lines of the diagonals and the corner curvatures as shown in Fig. 2.
In addition it should be noted that for rectangular frames the load points at the corners of the inner rectangle are dictated by the type of fitting employed and are usually off centre of the corner curvature (Figs. 2 and 10). The geometry is arranged such that is the horizontal length of the main frame and H the height.
In practice the proportions of the sides of the rectangle should not be greater than approximately 2:1 as otherwise the fitting of the corner loading points becomes difficult.
As cyclic testing has only been carried out on a square frame, ideally further testing should be carried out on rectangular frames to confirm their behaviour.  (4) and (5)  The absorber details are shown in Fig. 6.
Substituting in equations (4) and (5) for f = 255 MPa, gives for the first yield tion: This motion, together with additional motion to accommodate the deflection of diagonal rods, pins, etc. will be required at the jack to start yield.
This load gives the straight line OQy in Fig. 4 for the deflection up to 5 mm. This is a stiffer characteristic than that recorded in the tests, but bearing in mind that deflections were measured by a transducer in the jack ram and would include flexibilities of rods, pins, ram, etc. up to the jack, the characteristic is not unreasonable.
The value of yield load appears to be approximately correct as a narrow loop would be obtained at that load, the loop width being attributable to friction in the pins and on bearing pads supporting the frame weight.

Plastic Condition
Using equation (10)  (2) The shear load Q at first yield calculated from Equation (9 ) also agrees reasonably well with the test results.
(3) The value of the shear load Q to cause continuous movement of the joint of the absorber, as calculated from equation (11), gives a conservative estimate of the load capacity of the absorber.

Design Curves for Range of Shear Loads for Energy Absorption
Values of the shear load at yield, Qy, from equation ( 9 ) and the shear load for the fully plastic condition, Q , from equation (11), are plotted for a rSnge of bar sizes in Fig. 7, to indicate the design range of loading for energy absorption. Above Q the number of cycles to failure is reduced and a locking up condition may develop.

5.2
Design Curves for the Range of Deflections Associated with Energy Absorption

Yield Condition
The deflection s associated with first yield, obtained fRom equation (9), is shown plotted in Fig. 8 for a range of bar sizes.

Deflection Associated with Plastic Condition
Since the plastic theory of bending in its simplest form associates continuous yielding at the plastic yield stress f with no limit on deflection, resort has P to be made to practical testing in order to assess the likely deflection at peak energy absorption.
In the tests at PEL a jack motion of 100 mm, giving an overall frame deformation, S , of the same value, produced a hysteresis loop indicating a good absorption of energy; from previous testing this would correspond to a strain of about 3% at the extremes of the section of the bar in bending (3,4).
For the square of 610 mm side, the angular rotation of each joint is given by sin -1 100/610, i.e. 9.4 °, on the assumption that the shear deformation in the inner and outer squares has approximately the same value, which is true for small angles of rotation (see calculation para. 6.2 for an example of actual values).
If the size of the inner rectangle is reduced relative to the outer, then less shear deflection is required to produce the same angular rotation and the same energy absorption, i.e. the device becomes stiffer.
By proportion, for the same energy absorption the deflection for an absorber of height h is given by S = 0.lh/0.61 metres. P Also previous testing has indicated that a good energy absorption and a reasonable life is obtained for a strain of 3% at the extremes of the section. Evidently this strain is reached more rapidly as the bar size increases.
On the assumption that plane sections remain plane, then the most desirable shear deflection for bars of diameter d, when compared with 25 mm bars used in the test, is given approximately by: This relationship is shown plotted in Fig. 9 for a range of bar sizes and gives a rough indication of the def]ection required to produce good energy absorption.
The deflections S at first yield ace replotted from Fig. 8 y in Fig. 9 by way of comparison, and the deflections for the fully plastic condition are seen to be up to 50 times those at first yield, this value being approached when both the bar size and the height of the rectangle are comparatively small, i.e. d= 16 mm and h ' = 0 . 2 m.

General
Lock-up of the bracing occurs for gross deformation of the central rectangle when the geometric shortening of the diagonal dimension in the unloaded direction is significantly greater than that of the corresponding diagonal dimension of the outer rectangle. In the tests on the square frame at PEL, lock-up began when the lateral deflection of the jack reached ± 142mm (see Fig. 4), corresponding roughly to a rotation strain of sin -1 142/610, i.e. about 13°, in the twin 25 mm bars.
At the working deflection of ±10 0 mm, corresponding to about 9°, there was negligible lock-up.
Since deflections are designed to be less as the size of bar increases (Fig. 9) there is less chance of lock-up if larger bars are chosen.
However, in general, the problem does not appear to be one of practical significance as in the examples calculated so far optimum energy absorption occurs before lock-up.
In the tests carried out at PEL, the lock-up stresses did not cause overstress ana a further example of the calculation, for a practical design, is given below.

Calculation of Lock-Up Forces for a Typical Structure
The bracing shown in Fig. 10 was installed in a building by consultants Whitcher, Grant, King and Associates of Lower Hutt, the effective lengths of the absorber sides being l l = 480 and h' = 290 mm as shown for a pair of 20 mm rods. Also L = 4.8 m and H = 2.9 m.
Following through the design, Horizontal deflection s at first yield ( Fig. 8 and equation 9) y = 1.7 26 mm.

Horizontal deflection
Sp for peak energy absorption = 59.45 mm ( Fig. 9 and  Lateral load Qp for peak energy absorption ( Fig. 7 and equation 11 Neglecting direct strain within the inner rectangle this extension will be accommodated by strains in the diagonal rods, each having a length of 5.047 mr with some adjustment of the geometry of the framework. The self-straining stress will be given by The bracing method proposed is an extremely reliable way of providing earthquake resistance in structural panels in that testing (1) showed that many hundreds of cycles of loading could be completed repetitively without the development of slack in the bracing rods.
The design shear loads Q for large deformation (Fig. 7) are p conservative in that the work hardening effect during testing was shown to give peak shear loads above the values given on the graph.
The range of deflections ( Fig. 9) enable an estimate to be made of whether a particular bar size is acceptable from the point of view of inter-storey drift.
A locking-up effect occurs for gross deformation but this will normally be outside the range of contemplated design work.
However as this effect is often used in snubbers, shock absorbers, boat fenders, etc. it can be designed for, if required, by allocating sufficient area in the bracing rods to carry the direct tensile forces involved.