Section 04 - Steel

8/10/2019 Section 04 - Steel

1/5


2/5

)

Reinforced Concrete in Thirty Lectures 4-2

nec'ed region. %n terms of engineering strain" fracture occurs at a alue to $9 higher than the strain1corres#onding to ultimate stress.2

The stress-strain relationshi# in com#ression is a##roimately but not eactly the same as that in tension.4

%n design" it is assumed to be eactly the same.$

&Figure 4-2. Idealized Stress-Strain Characteristics of Reinforcing Bars)

*5 sim#le analog #roides us with a way to isuali3e the #henomena re#resented by the stress-strain cure+described. teel is a collection of /atoms.0 /5toms0 moe away from or closer to one another in1

res#onse to a##lied stress (Figure 4-4.a and Figure 4-.a! de#ending on the sense of the stress. %f the11 stress does not eceed the yield stress" the atoms tend to go bac' to their original locations as the a##lied12stress is reduced. 5fter yielding" atoms slide on inclined surfaces as shown in Figure 4-4.b and Figure14-.b. These relatie moements of atoms result in #ermanent changes in the structure and dimensions of14the element. %f one thin's of the sliding of atoms as being similar to the sliding of an ob:ect on a surface1$with friction" one could conclude that the force reuired to continue the relatie motion of atoms during1&

yielding would remain constant after sliding starts. ;ecause friction is usually inde#endent of the1)direction of motion" one should also e#ect the yield stress to be similar in tension and com#ression. The1*

friction analog hel#s us understand the #resence of #ermanent deformations after unloading. ;ut the1+analog fails to #roide us with an e#lanation for strain hardening. The interaction between atoms is2more com#le than im#lied by friction model.21

22

224

Figure 4-4. Atoms of Steel under

Compressie Stress

Figure 4-!. Atoms of Steel under

"ensile Stress


3/5

_

Reinforced Concrete in Thirty Lectures 4-

teel used as reinforcement for concrete is commonly aailable as hot-rolled bars with standard1geometrical and mechanical #ro#erties. The most commonly used bars are billet-steel bars. These bars2

hae fracture strains guaranteed to eceed &9 oer an *-in. gage length including the fracture. They are#roduced in three /grades0< 4" &" and )$. The grade refers to the s#ecified lower bound to the yield4

stress. =otice that what is s#ecified is a lower bound" not a mean or a median. o when we buy 8rade &$billet steel" the most widely used reinforcing steel" it is ery unli'ely that the actual yield stress is & 'si.&

%n most cases" the actual yield stress eceeds the nominal alue" the best estimate of the mean yield stress)ranging usually from &$ to )$ 'si.*

%n design" we assume that the yield stress"+fy" of 8rade & bars is & 'si.1

;illet-steel bars should not be welded11because welding ma'es them brittle. %f12

welding is reuired" low-alloy steel bars1should be used. Low-alloy steel bars14

ty#ically hae yield #oints between & 'si1$and &* 'si and elongations at ru#ture1&

eceeding 19 oer an *-in. gage length.1)

%n #ractice bars are identified by a1*#ound sign and the si3e of the nominal1+

diameter in eights of an inch. For eam#le.25 >* bar is a bar with a nominal diameter21of one in. i3es and nominal yield stresses22of bars > to >1* are mar'ed as shown in Figure 4-$.2

The unit stress-unit strain cures of reinforcing steel bars of different grades hae different sha#es (Figure24

4-&.!. The elongation at ru#ture is also different between one grade and another. %n general" steels with2$higher strengths tend to hae shorter yield #lateaus (if any! and smaller deformations at ru#ture.2&

Table 4-1 lists standard bar si3es" cross-2)sectional areas" and weights #er foot of2*length. The bars we use today hae2+surface deformations to im#roe their

bond with concrete. They are not1

#rismatic" and their actual cross-sectional2areas listed deiate from the areas ofcircles with diameters eual to the listed4diameters. For these reasons" we refer to$the dimensions in Table 4-1 as /nominal&

dimensions.0)

*tandard bars are sold in 2" 4 and &-ft+

lengths. ?andling at the construction site4 of indiidual bars weighing more than41a##roimately + lbf is considered to be42difficult.4

444$4&

4)

Figure 4-#. $nit Stress s $nit Strain for Bars of%ifferent &rade

Figure 4-'. Bar (ar)s

Billet


4/5

_

Reinforced Concrete in Thirty Lectures 4-4

1"a*le 4-1 +roperties of Standard Bars2

Bar SizeDiameter

[in.]Area[in

2]

Weight[lbf/ft]

3 0.375 0.11 0.37

! 0.50 0.20 0."

5 0.25 0.31 1.0!3

0.75 0.!! 1.502

7 0."75 0.0 2.0!!

" 1.00 0.7# 2.7

# 1.12" 1.00 3.!0

10 1.27 1.27 !.303

11 1.!1 1.5 5.313

1! 1.#3 2.25 7.5

1" 2.257 !.00 13.

4$&)

*+

111

Example12Consider a 1-foot long" 8rade &" billet-steel" >* bar sub:ected to tensile aial force. @raw an a##roimate1relationshi# between force and elongation.14

1$Solution1&The yield stress of the bar is between &$ and )$ 'si. The1)cross-sectional area is .)+ in2. Therefore" the force that1*ma'es the bar yield is between &$ .)+ A $1 'i# and )$ 1+.)+ A $+ 'i#. This is a##roimately eual to the weight of ten2#ic'u# truc's. ;ecause the modulus of elasticity is 2+ 121'si" the yield strain is between &$B(2+ 1! A .22 and22)$B(2+ 1! A .2&. The length of the bar is 1 feet A 122in. Therefore" the elongation at which the bar yields is24between .22 12 in. A .2& in. and .2& 12 in. A2$.1 in. 6e e#ect to hae strain hardening (in aerage! at an2&elongation of a##roimately .1 12 A 1.2 in. 6e e#ect2)the force-elongation relationshi# to be in the shaded region

2* shown in Fig. 4-).2+

Questions-a. Re#eat the eam#le for a 2-ft long" 8r.-&" billet-steel" >11 bar sub:ected to tensile aial force.1-b. Two 4-ft long bars are going to be lifted using a crane (one bar at a time!. ;oth bars are 8r. & bars. ne is a2>& bar and the other is a >11 bar. The crane has a s#reader beam that allows the crane o#erator to lift the bars fromtwo #oints. 5ssuming that forces a##lied to the bar by the lifting rig are ertical" recommend the locations of the4#oints where the lifting rig should be attached to the bars.$

Figure 4-, Force-longation Relationship of a

1-ft long/ &rade #/ A,#/ 0 *ar

Essentials:

$%rrentl& bar '%alit& i( i)entifie) b& the *gra)e+ ,f the bar- e.g.- *ra)e 0+ refer( t, a bar ith a minim%m&iel) (tre(( ,f 0 (i.

Bar (ize i( i)entifie) b& a n%mber that i( ar,imatel& e'%al t, the n,minal )iameter in eighth( ,f an inh.

Alth,%gh in ,net%al )e(ign the (tre((4(train relati,n(hi ,f reinf,ring bar( i( a((%me) t, be *ela(t,4la(ti-+ at%all& the bar ma& )eel, a (tre(( 1.5 time( the &iel) (tre(( if (traine) be&,n) the &iel) (train.

6rat%re (train f,r a ra)e 0 bar i( (eifie) t, eee) 0.0

Bar( ith &iel) (tre((e( higher than that ,f ra)e 0 bar( ten) t, hae (maller (train( at frat%re


5/5

)

Reinforced Concrete in Thirty Lectures 4-$

-c. %gnoring strain hardening (which is usually done in design! and assuming fyA&'si" com#ute the stresses1associated with the following strains

Documents

Section 04 - Steel