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268

Rul e (B) requ ires that the she ar c apac ity of a be am or a

column at any section must be greater than the max imu m shear

force that could be imposed on the member by an eart hqua ke, i.e.

M  M

( V + V ) p >

  (V +

  il

l  +

  ki

2

g — —

Where   V

c

  and V

u

 1

  are the ultimate shear forces carried by

the concrete and the stirrups respectively, Vg is the maximum

grav ity or trans verse shear applie d, and Mi +

  M 2

  is the

largest sum of opposite-sign ultimate moment capacities at the

ends of the mem ber . For columns Vg is zero and  M 2  may be the sum

of the ulti mate moment ca pacit ies of the beam s fram ing into the

top of the column, in the plane considered. These may all be

calc ulat ed by the formulae in Chap ter s 16, 17 and 19 of the 1963

A.C.I.  Building Code.

The form ulae for shear and ben din g show that the ul tim ate

resi stin g capac ity of a secti on is more or less pro por tion al

to the yield point of its reinforcing.

For compl ete safety, the resi stan ce to shear or ben ding mus t

be calcu lated on the lowest yield stres s, wh il e the applied shear

or bendi ng forces must be calculated on the maximum yield str ess .

Simil arly, to allow for defi cien cies in the concr ete or the

formulae, resistance must be decreased by  0 the undercapacity

facto r. Applied forces must be increased by what ever over

capacity may exist.

It is ther efore essenti al to kno w the maxim um as wel l as the

mini mum yield stresses of the reinforcement to be actually used.

For economy, these must be as close to each other as practicable.

Eco nom y may also be achieved by accepti ng a degr ee of risk .

The like lihoo d of low yield st irrups being combined with hig h

yield m ain bars can be calcu lated if the his tog rams of tests of

the steel bei ng used are ava ila ble . What degree of risk to

acce pt is diffi cult to deci de on, but it woul d have to be

appro priat e to the possible loss due to failure.

A further margin of strength can be found in the concrete

stre ngth , whi ch in all prob abil ity has advanced from its 28 day

stre ngth by a per cen tag e governed by curing condi tions and the

composition of the cement.

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Designers can stipulate in their Specification that the

minimu m yield stress of the reinforcem ent must be , say 40 ks i,

and the maximum 50 ks i. This requirement can be satisfied by

the supplier providing the appropriate test certificates.

How eve r, it is pos sibl e that some foreign bars may be in

advert ently used. It is theref ore better if the specified

limits wer e taken close to the actual limits of the steel

produced.

Fig . 1. gives average yield points and the limits wit hi n

wh ic h 9 5% of tests lie for rein forc ing to N. Z. S. S. 1693 and

N. Z .S

 .S.

  1879, for steel as produced by Pacific Steel Ltd.,

Otahu hu. The information is from a private communication from

the Compa ny and is indic ative onl y.

It should be noted that No.12 bars are not as yet defin ed

by N.Z. S. S. 1879 . Another line should be added to Table 3 of

that Standard.

Amendment No . 1, dated December 19 68, to N. Z. S. S. 1693 ,

rai sed the mini mum yiel d stress for steel to that Stand ard

from 33 ksi to 40 ksi.

No

3 4 5 6 7 8 9 10 11 12

B A R S I Z E

F i g

1