Publisher’s version / Version de l'éditeur:
Transactions of the Engineering Institute of Canada, 2, 3, pp. 129-131,
1958-11-01
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Relative strengths of plates on elastic foundation
Black, L. D.
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0c.C
TH1
N21r2
no.
72
c . 2
BLDG
NATIONAL RESEARCH COUNCIL
CANADA
DIVISION O F BUILDING RESEARCH
RELATIVE STRENGTHS OF PLATES
ON ELASTIC FOUNDATION
L. D.
Black
REPRINTED FROM
TRANSACTZONS OF THE ENGINEERING INSTITUTE OF CANADA
VOL. 2, NO. 3, SEPTEMBER 1958, P. 129-131
RESEARCH PAPER NO.
72
OF THE
DIVISION
OF BUILDING RESEARCH
A coupon system has been introcluced to nznks pc~yn~ents for publicn- tions relr~tioely simple. Coi~pons ore nouilnble i n tlenoininntions of 5, 25, ancl 50 cents, ancl tnny be obtninecl by making a remittance as inclicnterl abooe. These coc~pons n ~ n y be user1 for the purchnse of (111 National Research Cocincil ptiblicc~tions including specificutions of the Cnnadinn Gooernnzent Specificntions Bonrcl.
ie tip. The range went from as close ns possil~lc to t o about onc half 1 fro111 the tip
c shccts were thcn loaclcd t o fnilurc and the Iargcst
so a statistical procedure hael t o be adopted.
detailed rcsults of tl~csc es11el.imcnts are givcn in
uncertainty. Thc bearmg strengths :~ctually 01)-
ha11 about 1.5. The area of the fragments n a s tliviclccl and the sqnarc root c'~tractcc1 to proviclc a basis 011
t o elllibit the rcsults of these tests. This yicltlctl
Fig. 1-Relation of size of sanlple to ultinlate brealting strength.
1 " " " " " " ' l
Fig. 2-Dependenee of relative strength o n apex angle of seelorial plate.
picccs from t h c cdgc-loaded plates to cstiniate t h c strcligth of thc parcnt material.
Relative Strength of Edge-Loaded and Centre-Loaded Plates
The trrnl "strcngth inclcx" s11:lll be dcfinccl a s the hrcaking load tlivitlccl by thc square
of
the thickness of tllc sample. I n 'l'al)le I thc tcrnl "fmgmcnt" Incans thc piccc cut fro111 the m:ttcrial of the cclgc-loatlccl plate to furnish a11 csti~nate of the strength of thc parent m:ltcrial. L is tllc breaking load in pounds; t is tllc tliicliilcss ill inches.Table I. Results of l'euts ou Edge-Loacled Plates
Strcngtli L/L2 edge Sample Index L/t? Ratio L/l"arcnt Full Shcct 16,170 O.-L-LSI Edge(1) 7,230 Isclge(2) 7,250 0.4-137 Fragment (2) 16,340 Edge(3) 6,040 0.4203 Fmgment(3) 14r370 3/ 1.3121 0.4375
Thus the csti~llatc of strength of tlle cclgc-loatlccl platc in terms of t h a t of tllc centrc-loaclecl plate is 44 per ccnt.
A cliffcrcnt mcthocl of estimating thc sntllc qua~ltity is available. The lilenlls of the strength ind~ccs for tlic ccntre- loaclccl platc ant1 all four of tllc cclgr-loaclcd platcs are 15,240 anel 6.724 rcspcctivclj-. T1ic ratio of thcsc ~ i u n ~ b e r s is 0.441 or 41.1 pcr ccnt. Tlic :lgrccmcnt nit11 tlir fonnrr valuc of 0.438 confirms tllc v:llidity of thc experimental
results.
Using tlie tllcorctical argument given by Gold et a1 ant1
thc Poisson's ratio approprintc to glass, tllc strcngtli of the cdgc-loacletl platc as con11)ared to tliat of tllc centrc-loaded platr is 38.9 pcr crnt.
90° Seetorial Plate
The nleall of the s t r c ~ l g t h indices for t h e 90" sectorial
the average only 1.4 per cent of t h e tirlle and not 1/13
A list of nll pr~blicotior~s o f tlze Dit;ision of Rr~ilding Research is available clrtd I I K I I J 11s obtc~ined fiorn the Prlhliccltions Section, Dit;ision
