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OVER-REINFORCED BEAM
First of all, it has been done an analysis about the inuee of
thereinfore!ent on the bea!"s dutility# For this $ro$ose, % ases
&eree'aluated( the tutorial ase )* steel bars of +!!*., a
reinfored bea!&ith */ steel bars of +!!*, and a reinfored bea!
&ith */+0 steel barsof +!!*# Figure 1sho&s the
load-dis$lae!ent ur'e obtained#
# *# 1# # 2# +##
*#1#
#
2#
+#
+*#
+1#
3oad - Dis$lae!ent
*/+ steel
*/+0 steel
*/ steel
Dis$lae!ent )!!.
3oad )4N.
Figure 1:Load-displacement curve obtained.
It an be a$$reiated ho& the inre!ent of the reinfore!ent
!a5es alsoinreasin6 the failure load fro! 7+#%2 4N in the 8rst ase
to ++#7 4N in the
seond and to +%+#1 4N in the third one# 9hat entails a *+: and a
11:res$eti'ely# In the sa!e &ay, it is sho&ed ho& the
hi6hest load su$$ortedis bi66er in the reinfored ase, but the
dis$lae!ent until reahin6 theinelasti ;one is lo&er, 6oin6 fro!
1#*2!! to %#%%!! and *#%7!!res$eti'ely# 9hus, it an be seen the
inre!ent of the dutility &ith thereinfore!ent#
For this ourse&or5 the referene has been the */+0 steel bars
reinforedbea! and the three $ara!eters to study &ere ha'e been(
!esh si;e,frature ener6y and shear retention fator#
9he analysis of the !esh si;e has been arried out studyin6 %
ases( s!all
!esh )#+!., ori6inal !esh )#2!. and bi6 !esh )#*!.#
3oad-dis$lae!ent ur'es are sho&n in Figure 2.
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# *# 1# # 2# +# +*##
*#
1#
#
2#
+#
+*#
+1#
+#
3oad - Dis$lae!ent
Nor!al Mesh
Bi6 Mesh
Dis$lae!ent )!!.
3oad )4N.
Figure 2:Curva Carga-Desplazamiento para los 3 tipos de
malla.
It an be a$$reiated ho& the % !eshes si!ulate &ith
sureness the linealbeha'ior ;one of the $roble!a# 9a5in6 the
s!allest !esh as the !ostaurate one, the !=/i!u! load 'aries fro!
+*+#7 4N to +%+#1 for theori6inal one and +%7#0 4N for the bi66est
one, entailin6 an 2: and a +1:de'iation# It>s &orthy to
distin6uish that the s!allest !esh &as 2 ti!ess!aller than the
ori6inal one and has i!$ro'ed an 2:, &hile on the otherhand the
bi66est !esh &as ?ust *#0 bi66er and its result has 6one to a
+1:o'er the $redited# Further!ore, in the non-linear ;one the
bi66est !eshdoes not follo& the !ain trend of the other
t&o#
9he bi66est dis$lae!ent 6i'en di@ers in funtion of the ase,
bein6 bi66erfor the bi66er !esh# ith the s!all !esh is 2# !!, 2#00
!! &ith theori6inal one and ++#0 !! &ith the bi66est one
that !a5es a : and a1%: res$eti'ely# In this ase it an be seen
ho& the bi66est !esh 6etstotally disarded, bein6 that the
nu!erial result and the trend, both di@erfro! the e/$eted
results#
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Figure 3:Displacements for original (1), big (2) and small (3)
mes.
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Figure 4sho&s the ra5 $attern after
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For the Frature Ener6y )FE. analysis it has been ta5en as
standard 'aluethe one 6i'en in the tutorial )#*%0/+ -0MN!.# Fro!
this 'alue, in has been6enerated t&o ases &ith lo&er
FE( 0#++0/+ -0 MN! )7:. and 1#%/+-0 MN! )0:. and three ases
&ithhi6her FE( #2020/+ -0 MN! )++:.,#7%2/+-0 MN! )+*0:. and
+*#10/+-0 MN! )*:.# Figure 5 sho&s the
load-dis$lae!ent ur'es#
# *# 1# # 2# +##
*#
1#
#
2#
+#
+*#
+1#
3oad - Dis$lae!ent
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Figure 7:Crac! pattern and displacements for standard, %&'
and 2' #$.
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Finally, it has been analy;ed the beha'ior of the o'er-reinfored
bea!han6in6 the shear retention fator# Ori6inaly, this fator
&as Gy$erbola AH,ha'in6 t&o !ore o$tions( Gy$erbola BH and
G3inearH# Figure 8sho&s theload-dis$lae!ent for the % ases#
# *# 1# # 2# +# +*##
*#
1#
#
2#
+#
+*#
+1#
3oad - Dis$lae!ent
y$erbola A
3inear
y$erbola B
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Figure 9:Crac! pattern and displacements for iperbola *,
+perbola , Lineal and
zero sear retention factor.
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CONC3J
