Model tests on reinforced plywood roof beams

ii

'SfB Gi 2 Build. Sci. Vol. 2. pp. 123.131. Pergamon Press 1967. Printed in Great Britain

I

Model Tests on Reinforced Plywood Roof Beams D. BOND,* Ph.D., M.I.C.E.

Plywood roof beams are described which are reinforced top and bottom with steel bars. These bars are curved so that they meet at the beam supports where they are welded together. In this manner the bond stresses and shearing stresses in the timber are reduced. A method of analysis is presented by which the stresses in these beams can be calculated. Theoretical values are compared with experimental results which were obtained from tests on scale models of these beams

INTRODUCTION

load of 30 lbf/ft 2 of roof area over an effective span of 60 ft, the beams being at 20 ft centres. A t-scale model of this beam was made and tested. The method of construction of both types of model was the same: The timber casings which surrounded the reinforcing bars were glued to plywood strips. It was intended that these strips would resist lateral splitting of the casings, vertical splitting being resisted by the plywood webs. Grooves were machined in them. The reinforcing bars were placed in the casings which were glued and damped together while they were still straight and before the top and bottom bars were welded together at beam supports. It was assumed that in practice such reinforced timber strips could be produced in quantities separately. These strips were bent to the correct shape and the ends of the reinforcement were welded together. The stiffeners were glued to one plywood web and the reinforced assembly was glued in position. Plain butt joints were used between this assembly and the stiffeners. All curved reinforcement was bent to a parabolic shape, this being most suited to supporting a uniformly distributed load over the whole of each beam. GK60t high yield steel ribbed reinforcing bars and Cascamite ' O n e Shot' synthetic resin wood glue were used in all beams, the bonding of the bars depending on the mechanical grip of the timber on them. Finnish birch plywood with the grains in its outer veneers everywhere parallel to the span and yellow pine were used for making these models. The latter was considered necessary in an attempt to avoid flaws which would cause faulty readings, particularly of strain gauges; a cheaper timber would be more suitable in practice. The moisture contents of the plywood and pine were approximately

THE BENDING resistance of plywood beams can be increased if they are reinforced top and bottom with steel bars. But if the top and bottom reinforcing bars are parallel the bond stresses and shearing stresses in the timber can be excessive, causing unacceptable creep under long-term loading and an inadequate ultimate strength. It has been shown previously[l] that efficient reinforced plywood beams can be made if the top and bottom reinforcing bars are curved so that they meet at the beam supports where they are welded together. Being inclined near the ends of the beams they are able to resist a considerable part of the shearing forces, thus reducing the bond and shearing stresses in the beams. In order to examine the problems which might arise if this type of beam were used over moderately large spans, two roof designs were considered: Beams 1 were designed to support a total load of 25 lbf/ft 2 of roof area over an effective span of 36 ft. The plywood roof sheathing was to be supported on timber purlins which were to span between the reinforced plywood beams, the latter being at 15 ft centres. The sheathing was to be covered with mineral-finish roofing felt and a plastic-coated plaster board ceiling was to be attached to the purlin soffits. This design is illustrated in figure 1. A ~-scale model of this roof was constructed and tested[2]. In an attempt to simplify the method of attaching purlins, beams 2 were designed to support a total * Civil Engineering Department, The Queen's University of Belfast. I" Supplied by G. K. N. (Northern Ireland) Ltd. 123

D. Bond

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Model Tests on Reinforced Plywood Roof Beams

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126

8~ and 9~- per cent respectively when the beams were tested. Quantities of steel bars and timber (not including wastage but allowing for scarfed joints and additional web thickness at beam supports) would be as shown in Table 1.

Compatibility of strains 1

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Model Tests on Reinforced Plywood Roof Beams

127

Fig. 5. Beam I under test.

Equation 5 was solved as a jury problem. An Algol program was written for this purpose. The solution of this equation gave values of force P at all positions along each beam. An approximation was made to include part of the roof sheathing in the computations for beams 2. The flange force F can be found by substituting values of P in the third part of equation (1). The bond stress and shearing stresses in the web can be found at any point from values of dP/dx and dF/dx. Although the deflections can be found by integrating 1/R from equation (2), they can be calculated with sufficient accuracy for practical purposes using elementary bending theory as described later.

A l-scale model roof was made which included two beams of type 1, purlins and roof sheathing. The full working load was placed on this model (figure 7). It was subjected to a creep test until no further deflection was recorded. It was again tested under its full dead load but with its live load of 15 lbf/ft 2 of roof area on one side only of midspan. The results are shown in figure 8. One of the beams was removed together with a sufficient width of roof sheathing and purlin ends to give it lateral stability. It was tested to failure by being subjected to the 16-point loading which is shown in figure 5. Its midspan deflection was measured (figure 9). The model of beam 2 was tested in a similar manner (figure 10).

EXPERIMENTAL RESULTS One of each type of model beam was tested within its working range by being freely supported and subjected to a 16-point loading which was equivalent to a uniformly distributed load. The testing equipment is shown in figure 5 and is described elsewhere[3]. The forces in the reinforcing bars were measured using electric resistance strain gauges. These beams were subjected to other types of loading and computed and measured values are compared in figure 6. The model of beam 2 was tested together with a 12 in. width of roof sheathing attached to it, the model of beam 1 being tested within its working range without sheathing. The duration of each test was approximately 1 h and each beam returned to its original shape when the load was removed. The end supports moved apart approximately 0.09 in. when each model was subjected to its full working load.

CONCLUSIONS Each beam was designed on the assumption that the midspan bending moment due to the full working load was resisted by the steel only which was assumed to be at a working stress of 30 000 lbf/in 2. The actual stresses in the steel bars were less than this (figure 6). The mean stresses in the timber casing and supporting plywood (grains parallel to span) were approximately 5.7 and 9 per cent of the corresponding steel stress respectively. In each type of beam this casing and its supporting plywood contributed approximately 18 per cent of the total force P (before creep), the remainder being contributed by the steel. The tests to failure of the scale models of beams 1 and 2 indicated that their factors of safety would be 3-94 and 2.96 respectively (figures 9 and 10). At failure the compression steel of beam 1 buckled laterally at midspan;

128

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Model Tests on Reinforced Plywood Roqf Beam~

129

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failure might not have occurred thus if the beam had been an integral part of the complete roof. The compression reinforcement of beam 2 buckled vertically adjacent to midspan. When they were subjected to their working live loads the midspan deflections of these beams were less than span/360 (figures 9 and I0). On the assumption that this limitation of the live load deflection[4] can be applied to these plywood beams, their depth/span ratios would appear to be adequate; in fact beam 2 could have been more slender. The midspan deflection can be estimated approximately by elementary bending theory, assuming a variable moment of inertia throughout the length of the beam. The results of these calculations compared with measured deflections are given in Table 2. Table 2

Beam

Midspan deflection : measured/calculated

1

1.05

2

0'99

The creep tests on the ½-scale model roof which included two beams of type 1 indicated that under its sustained full working load its midspan deflection was not excessive. The plywood sheathing was attached to the beams to give them lateral stability. The fluctuations of midspan deflections were attributed to the movement of the sheathing with a variation of its moisture content due to changing climatic conditions. The model of beam 1 which was not broken was measured 3 months after its load had been removed and it appeared to have returned completely to its original shape. The manufacturing costs of these and other roofing beams have not yet been compared. But their weights compare favourably with those of castellated steel beams and high yield universal beams when they are supporting the same loads.

The results of these tests indicate that the steel reinforcement was utilised more effectively in beam type 1. The steel stresses under its working load were greater and there was a higher factor of safety; vertical buckling of the compression reinforcement was resisted by the better bond between the plywood webs and the timber casing surrounding the bars and a closer spacing of stiffeners. On the other hand this type of beam is narrower than beam 2 and the problem of purlin end supports which this causes must be examined further. Because previous beams[5] failed in shear at their supports, additional web thickness was provided at the ends of the beams which are described in this paper. This was not included in the elastic computations which would not in any case apply to the conditions at ultimate load. Whether this precaution was necessary requires further examination. Consideration should be given to increasing the actual working stresses in the steel reinforcement. But since this would also increase the stresses in the surrounding timber, the influence which this would have particularly on creep and buckling should be examined. As creep occurs in the timber the stresses in the steel reinforcement increase. No special attention was given to the selection of the best glue for these beams and this problem including the protection of steel against corrosion requires further study. These tests have shown that further consideration should be given to incorporating these beams in suitable structures. Particular atteation should be given to constructional details, the t ~ i ~ o f 1 1 t ~ which are most suitable and to methods of m ~ t facture. Shapes of roofs in which ~ ~ be most economically used ~ 1~ ~ and further tests on scale models of such beams are recommended. Acknowledgement--The author acknowledges with gratitude the encouragement of Professor T. M. Charlton, Head of the Civil Engineering Department, Queen's University of Belfast, where this work was carried out.

Model Tests on Reinforced Plywood Roof Beams

131

NOTATION A~ = cross-sectional area of top flange = cross-sectional area of bottom flange. A~p = cross-sectional area of steel in top reinforcement = cross-sectional area of steel in bottom reinforcement. A,p = cross-sectional area of timber strips surrounding reinforcement. D = Distance between centres of top and bottom flanges at any distance x from midspan. DI = distance between centres of top and bottom flanges at midspan. D2 = distance between centres of top and bottom flanges at supports. dp = distance between centres of top and bottom reinforcement at midspan. E~ = modulus of elasticity of steel. E, = modulus of elasticity of timber. F = force in top flange = force in bottom flange. G = modulus of rigidity of plywood based on total web thickness z.

L = effective span. M = bending moment at distance x from midspan. p = total force in top steel bars and timber strips surrounding them = total force in bottom steel bars and timber strips surrounding them. R = radius of curvature of neutral axis at distance x from midspan. S = shearing force at distance x from midspan. y = distance from centre of flange to centre of reinforcement at distance x from midspan. Z = total thickness of plywood in webs. = slope of reinforcement at distance x from midspan. = slope of flanges (slopes relative to neutral axis). /3 ~' = shearing strain in webs at distance x from midspan. ~i = direct strain in flanges at distance x from midspan. ~ = direct strain in reinforcement at distance x from midspan. ~" = shearing stress in webs at distance x from midspan.

REFERENCES 1. D. BOND, Reinforced plywood beams, Cir. Engng. publ. Wks Rev. 60, 711 (1965). 2. A. HAMILTON, Design of 36 ft span reinforced plywood roof beam, Final Year Hons. Res. Project, Queen's Univ. of Belfast (1966). 3. D. BOND, Beam testing equipment, Tech. Educ. Indust. Training, 8, 2 (1966). 4. British Standard 449:1959, The use of structural steel in building (amended 1964). 5. D. BOND, Reinforced timber beams, Cir. Engng. publ. Wks. Rev. 61, 723 (1966).

Les p o u t r e s de toits en bois c o n t r e p l a q u 6 s o n t d6crites, renforc6es en h a u t et en bas a v e c les b a r r e s en acier. Ces b a r r e s s o n t ploy6es d ' u n e f a q o n p e r m e t t a n t de r6aliser j o n c t i o n a v e c les b a r r e s d ' a p p u i , ofa elles son soud6es e n s e m b l e . D e cette m a n i 6 r e , les t e n s i o n s de liason, d a n s les pi6ces en b o i s - - d i m i n u e n t . U n e m 6 t h o d e a n a l y t i q u e est d o n n 6 e d e v a n t servir au calcul de ces p o u t r e s . Les v a l e u r s t h 6 o r i q u e s s o n t c o m p a r 6 e s a v e c celles, o b t e n u e s e x p 6 r i m e n t a l e m e n t , l o t s des essais sur les mod61es r6duits de ces poutres. F u r n i e r h o l z d a c h b a l k e n sind b e s c h r i e b e n die o b e n u n d u n t e n m i t Stahlst/iben verst/irkt sind. D i e s e St~tbe sind so g e b o g e n , d a b sie sich a n d e n BalkenstiJtzen treffen, w o sie z u s a m m e n g e s c h w e i 6 t w e r d e n . A u f diese W e i s e w e r d e n die H a f t s p a n n u n g e n v e r m i n dert. E i n e a n a l y t i s c h e M e t h o d e ist eingeftihrt, m i t d e r e n H i l f e diese S p a n n u n g e n b e r e c h n e t w e r d e n k 6 n n e n . D i e t h e o r e t i s c h e n W e r t e sind m i t d e n V e r s u c h s w e r t e n , die bei E r p r o b u n g e n a n e i n e m v e r k l e i n e r t e n M o d e l dieser B a l k e n e r h a l t e n w u r d e n , vergliechen.