applied
sciences
A icle
Expe imen al S udy on he To sional Beha iou o
P es essed HSC Hollow Beams
Luís Be na do 1,* , Sé gio Lopes 2and Ma alda Teixei a 1
1Depa men o Ci il Enginee ing and A chi ec u e, Cen e o Ma e ials and Building
Technologies (C-MADE), Uni e si y o Bei a In e io , 6201-001 Co ilh
ã
, Po ugal; [email p o ec ed]
2
Depa men o Ci il Enginee ing, Cen e o Mechanical Enginee ing, Ma e ials and P ocesses (CEMMPRE),
Uni e si y o Coimb a, 3030-788 Coimb a, Po ugal; [email p o ec ed]
*Co espondence: [email p o ec ed]
Recei ed: 23 Decembe 2019; Accep ed: 13 Janua y 2020; Published: 16 Janua y 2020


Abs ac :
This a icle desc ibes an expe imen al p og am de eloped o s udy he in luence o
longi udinal p es ess on he beha iou o high-s eng h conc e e hollow beams unde pu e o sion.
The p e-c acking, he pos -c acking and he ul ima e beha iou a e analysed. Th ee es s we e ca ied
ou on la ge hollow high-s eng h conc e e beams wi h simila conc e e s eng h. The a iable s udied
was he le el o longi udinal uni o m p es ess. Some impo an conclusions on di e en aspec s o
he beams’ beha iou a e p esen ed. These conclusions, conside ed impo an o he design o box
b idges, include he in luence o he le el o p es ess in he c acking and ul ima e beha iou .
Keywo ds: conc e e s uc u es; beams & gi de s; o sion; high-s eng h conc e e; p es essing
1. In oduc ion
Pu e o sion does no eally occu oo o en in conc e e s uc u es; i usually occu s oge he wi h
o he in e nal o ces such as shea , bending and axial o ces. Howe e , in some s uc u es, such as he
case o cu ed box b idges, he o sional ac ion can be e y impo an o design.
The applica ion o p es ess usually inc eases he c acking and ul ima e esis ances o conc e e
s uc u es. P es ess is pa icula ly impo an in High-S eng h Conc e e (HSC) s uc u es. In gene al,
HSC s uc u es a e expec ed o be mo e lexible han No mal-S eng h Conc e e (NSC) s uc u es
because o he smalle c oss-sec ion a ea o membe s. This high lexibili y could be p oblema ic o
he se iceabili y limi s a es. The use o he p es ess echnique can also help o sol e such p oblems
associa ed wi h high lexibili y.
The applica ion o longi udinal p es ess in membe s unde high o sional loads is a common
si ua ion, as o ins ance in cu ed b idges. Many o such s uc u es a e also buil wi h HSC and use
hollow c oss-sec ions o he gi de s (Figu e 1) because hey p esen some ad an ages when compa ed
o solid c oss-sec ions. In la ge c oss-sec ions unde high o sion, he in e nal shea low is mainly
abso bed by he ou e conc e e shell. Thus, he conc e e a he cen e zone o he c oss-sec ion is
edundan and can be emo ed. As a consequence, hollow c oss-sec ions allow o a high educ ion in
weigh and conc e e consump ion, wi hou comp omising he o sional s eng h.
Appl. Sci. 2020,10, 642; doi:10.3390/app10020642 www.mdpi.com/jou nal/applsci
Appl. Sci. 2020,10, 642 2 o 14
Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 o 14
Figu e 1. Example o a hollow (box) c oss-sec ion o he gi de o a b idge deck.
The e a e s ill ew expe imen al s udies on hollow beams unde pu e o sion epo ed in he
li e a u e and mos o hem in ol e only a small numbe o NSC beams [2–5]. Only some ew ecen
wo ks epo new esul s o bo h NSC and HSC hollow beams [6,7]. When compa ed wi h NSC
beams, such s udies demons a e some o he ad an ages o HSC, namely, o inc ease he c acking
and ul ima e o sional s eng hs, as well as he o sional s i ness o he beams. Howe e , some
disad an ages o using HSC a e also poin ed ou , in pa icula ela ed o he o sional duc ili y which
cons i u es an impo an p ope y o be conside ed o design. By using he expe imen al esul s
epo ed in he p e iously e e ed expe imen al s udies and also by using nume ical models, o he
ecen s udies show ha some duc ili y can be obse ed in NSC beams unde o sion, namely o a
ce ain ange o he o sional ein o cemen . Howe e , almos no o sional duc ili y in HSC beams
unde o sion is obse ed [8–10]. Such s udies also show ha he le el o he obse ed o sional
duc ili y is no mally low when compa ed wi h lexu al duc ili y [11,12].
Few p e ious s udies leading wi h es ing o p es essed conc e e ec angula beams unde
o sion can be ound in he li e a u e, namely—Mi chell and Collins in 1974 [4], El-Degwy and
McMullen in 1985 [13], Hsu and Mo in 1985 [14] and Wa a e al. in 1995 [15]. Among he beams es ed
in he e e ed s udies ( wen y-se en beams), only h ee whe e hollow and buil wi h NSC. This is
because building hollow beams o es ing is mo e complica ed when compa ed wi h solid beams.
Fu he mo e, due o he complexi y o he expe imen al p og am, only a cons an longi udinal
p es essing was conside ed in all he e e ed s udies. The au ho s did no ind any p e ious s udy
on he expe imen al beha iou o HSC p es essed hollow beams unde o sion.
F om he o egoing, expe imen al s udies on he beha iou o p es essed hollow beams unde
o sion a e needed, in pa icula o HSC beams. This a icle p esen s an expe imen al s udy on he
global beha iou o HSC hollow beams wi h uni o m longi udinal p es ess. The beams we e loaded
unde pu e o sion and es ed up o ailu e. As o he p e ious e e ed s udies, a uni o m
longi udinal p es ess was applied. This was conside ed o be su icien o gi e some indica ions on
he in luence o p es ess on he beha iou o HSC hollow beams unde o sion.
2. Expe imen al P og am
2.1. Tes Specimens
Fo his s udy, h ee hollow beams we e es ed up o ailu e. The beams had a squa ed c oss-
sec ion and we e 5.90 m long. Du ing es ing, he beams had an ex emi y ixed o he s ong loo o
he labo a o y and he load was applied o he o he ex emi y by an elec omechanical ac ua o . In
his ex emi y, a special de ice ans o med he linea poin load applied by he ac ua o in o a o que
applied o he beam ex emi y. The dimensions o he es models a e p esen ed in Figu e 2. The
geome y and dimensions o he adop ed c oss-sec ion a e in line wi h some o he wo ks p e iously
e e ed and leading wi h hollow beams.
Ex e nal p es essing was applied h ough ou 0.6′′ wi es (0.6 inches o 1.52 cm diame e )
cen ed in he c oss-sec ion (Figu e 2). The o sional ein o cemen a io was kep cons an o he
h ee beams and i co esponds o an a e age alue which was de ined accoun ing o he ange o
alues ha we e used in a p e ious expe imen al wo k on simila beams wi h no p es essing [6].
Figu e 1. Example o a hollow (box) c oss-sec ion o he gi de o a b idge deck.
Since he end o he las cen u y, i is well known ha he uniaxial s ess-s ain cu e o HSC
is qui e di e en om ha o NSC [
1
]. The e o e, i is no ob ious ha he compu ing and design
models o HSC membe s can be di ec ly ex apola ed om NSC. Nowadays, many codes o p ac ice
al eady include HSC ange. Howe e , some aspec s o he s uc u al beha iou o HSC membe s s ill
need o be s udied in o de o check i he physical models accep ed o NSC can be adop ed o HSC.
The esponse o HSC beams o o sional loads cons i u es an example o such cases.
The e a e s ill ew expe imen al s udies on hollow beams unde pu e o sion epo ed in he
li e a u e and mos o hem in ol e only a small numbe o NSC beams [
2
–
5
]. Only some ew ecen
wo ks epo new esul s o bo h NSC and HSC hollow beams [
6
,
7
]. When compa ed wi h NSC beams,
such s udies demons a e some o he ad an ages o HSC, namely, o inc ease he c acking and ul ima e
o sional s eng hs, as well as he o sional s i ness o he beams. Howe e , some disad an ages o
using HSC a e also poin ed ou , in pa icula ela ed o he o sional duc ili y which cons i u es an
impo an p ope y o be conside ed o design. By using he expe imen al esul s epo ed in he
p e iously e e ed expe imen al s udies and also by using nume ical models, o he ecen s udies
show ha some duc ili y can be obse ed in NSC beams unde o sion, namely o a ce ain ange o
he o sional ein o cemen . Howe e , almos no o sional duc ili y in HSC beams unde o sion is
obse ed [
8
–
10
]. Such s udies also show ha he le el o he obse ed o sional duc ili y is no mally
low when compa ed wi h lexu al duc ili y [11,12].
Few p e ious s udies leading wi h es ing o p es essed conc e e ec angula beams unde o sion
can be ound in he li e a u e, namely—Mi chell and Collins in 1974 [
4
], El-Degwy and McMullen in
1985 [
13
], Hsu and Mo in 1985 [
14
] and Wa a e al. in 1995 [
15
]. Among he beams es ed in he e e ed
s udies ( wen y-se en beams), only h ee whe e hollow and buil wi h NSC. This is because building
hollow beams o es ing is mo e complica ed when compa ed wi h solid beams. Fu he mo e, due o
he complexi y o he expe imen al p og am, only a cons an longi udinal p es essing was conside ed
in all he e e ed s udies. The au ho s did no ind any p e ious s udy on he expe imen al beha iou
o HSC p es essed hollow beams unde o sion.
F om he o egoing, expe imen al s udies on he beha iou o p es essed hollow beams unde
o sion a e needed, in pa icula o HSC beams. This a icle p esen s an expe imen al s udy on he
global beha iou o HSC hollow beams wi h uni o m longi udinal p es ess. The beams we e loaded
unde pu e o sion and es ed up o ailu e. As o he p e ious e e ed s udies, a uni o m longi udinal
p es ess was applied. This was conside ed o be su icien o gi e some indica ions on he in luence o
p es ess on he beha iou o HSC hollow beams unde o sion.
2. Expe imen al P og am
2.1. Tes Specimens
Fo his s udy, h ee hollow beams we e es ed up o ailu e. The beams had a squa ed c oss-sec ion
and we e 5.90 m long. Du ing es ing, he beams had an ex emi y ixed o he s ong loo o he
labo a o y and he load was applied o he o he ex emi y by an elec omechanical ac ua o . In his
Appl. Sci. 2020,10, 642 3 o 14
ex emi y, a special de ice ans o med he linea poin load applied by he ac ua o in o a o que applied
o he beam ex emi y. The dimensions o he es models a e p esen ed in Figu e 2. The geome y and
dimensions o he adop ed c oss-sec ion a e in line wi h some o he wo ks p e iously e e ed and
leading wi h hollow beams.
Ex e nal p es essing was applied h ough ou 0.6
00
wi es (0.6 inches o 1.52 cm diame e ) cen ed
in he c oss-sec ion (Figu e 2). The o sional ein o cemen a io was kep cons an o he h ee beams
and i co esponds o an a e age alue which was de ined accoun ing o he ange o alues ha we e
used in a p e ious expe imen al wo k on simila beams wi h no p es essing [
6
]. The conc e e s eng h
was app oxima ely cons an , a ying be ween 77.8 and 80.8 MPa. The a e age le el o s ess in conc e e
induced by p es ess (
cp
) a ied be ween 0 MPa (beam wi h no p es ess) and 3.08 MPa, a e sho
e m losses. The maximum alue is no e y high because he losses we e somewha impo an . This is
because he e ec o ancho age slip becomes impo an when he leng h o he wi es is ela i ely small.
Figu e 2. Geome y and de ailing o es beams.
Table 1summa izes he cha ac e is ics o each es beam, namely— he eal hickness o he walls
o he c oss-sec ion (
), he dis ance be ween pa allel b anches o s i ups,
x1
and
y1
, he o al a ea
o o dina y longi udinal ein o cemen (
Asl
), he a ea o one b anch o he ans e se ein o cemen
(
As
), he longi udinal spacing o he s i ups (
s
), he o al a ea o p es ess longi udinal ein o cemen
(
Asp
), he a ios o longi udinal ein o cemen (
ρl=Asl/Ac
, whe e
Ac=xy
and
x=y=
60
cm
)
and ans e se ein o cemen (
ρ =As u/Acs
, whe e
u=
2
(x1+y1)
), he o al a io o ein o cemen
Appl. Sci. 2020,10, 642 4 o 14
(
ρ o =ρl+ρ
), he balanced a io o he longi udinal o ans e se ein o cemen (
mb=Asls/As u
) and
he a e age alues o he comp essi e conc e e s eng h ob ained om cylind ical specimens ( c).
The beams a e named acco ding o he se ies o which hey belong (se ies D) and o he a e age
s ess (in MPa) in conc e e induced by p es ess, cp, a e sho e m losses.
Table 1. P ope ies o es beams.
Beam. cm x1
cm
y1
cm
Asl
cm2
As
cm2
Asp
cm2
s
cm
ρl
%
ρ
%
ρ o
%mb c
MPa
c m
MPa
Ec
GPa
D-0 10.9 53.5 53.7
23.75
0.79 0 7.0 0.66 0.67 1.33 0.99 77.8 4.33 40.7
D-1.79 11.4 54.3 54.2
23.75
0.79 5.60 7.0 0.66 0.68 1.34 0.97 80.8 4.43 41.1
D-3.08 11.5 55.0 54.6
23.75
0.79 5.60 7.0 0.66 0.68 1.34 0.96 78.8 3.66 37.4
2.2. Ma e ials P ope ies
The a e age alue o he comp essi e conc e e s eng h used in each es ed beam was ob ained
om 5 cube specimens, cas ed and es ed a he same ime o he co esponding beam. The equi alen
cylind ical alues we e compu ed by ollowing he indica ions om Eu ocode 2 [
16
]. Table 2p esen s
he conc e e mix design used o p oduce he conc e e.
Table 1also p esen s, o each es ed beam, he a e age alues o he ensile conc e e s eng h
(
c m
) and o he conc e e Young’s Modulus (
Ec
). These wo pa ame e s we e compu ed om
c
also
ollowing he indica ions om Eu ocode 2 [16].
As example, Figu e 3illus a es a s ess (
σ
)–s ain (
ε
) cu e eco ded du ing he es o one o
he conc e e samples. The ini ial pa o he g aph shows he in luence o he adjus men due o he
exis en gap be ween he loading pla es o he es machine and he conc e e specimen.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 o 14
The beams a e named acco ding o he se ies o which hey belong (se ies D) and o he a e age
s ess (in MPa) in conc e e induced by p es ess,
cp
, a e sho e m losses.
Table 1. P ope ies o es beams.
Beam.
cm
1
x
cm
1
y
cm
s
l
A
cm
2
s
A
cm
2
s
p
A
cm
2
s
cm
ρ
l
%
ρ
%
ρ
o
%
b
m
c
MPa
c m
MPa
c
E
GPa
D-0 10.9 53.5 53.7 23.75 0.79 0 7.0 0.66 0.67 1.33 0.99 77.8 4.33 40.7
D-1.79 11.4 54.3 54.2 23.75 0.79 5.60 7.0 0.66 0.68 1.34 0.97 80.8 4.43 41.1
D-3.08 11.5 55.0 54.6 23.75 0.79 5.60 7.0 0.66 0.68 1.34 0.96 78.8 3.66 37.4
2.2. Ma e ials P ope ies
The a e age alue o he comp essi e conc e e s eng h used in each es ed beam was ob ained
om 5 cube specimens, cas ed and es ed a he same ime o he co esponding beam. The equi alen
cylind ical alues we e compu ed by ollowing he indica ions om Eu ocode 2 [16]. Table 2 p esen s
he conc e e mix design used o p oduce he conc e e.
Table 1 also p esen s, o each es ed beam, he a e age alues o he ensile conc e e s eng h (
c m
) and o he conc e e Young’s Modulus (
c
E
). These wo pa ame e s we e compu ed om
c
also ollowing he indica ions om Eu ocode 2 [16].
As example, Figu e 3 illus a es a s ess (
σ
)–s ain (
ε
) cu e eco ded du ing he es o one o
he conc e e samples. The ini ial pa o he g aph shows he in luence o he adjus men due o he
exis en gap be ween he loading pla es o he es machine and he conc e e specimen.
Figu e 3. Uniaxial
σ
–
ε
cu e o conc e e.
Table 2. Conc e e mix design (con en s pe m
3
).
Componen s Dosage
Thin sand 164 kg
Thick sand 908 kg
C ushed G ani 5–11 mm 734 kg
No mal Po land Cemen (C): Type I/42.5R 375 kg
Admix u e—Rheobuild 1000 4.8

Silica Fume (Sikac e e HD) 41 kg
Wa e (A) 145

A/(C + Addi ions) 0.35
Figu e 3. Uniaxial σ–εcu e o conc e e.
Table 2. Conc e e mix design (con en s pe m3).
Componen s Dosage
Thin sand 164 kg
Thick sand 908 kg
C ushed G ani 5–11 mm 734 kg
No mal Po land Cemen (C): Type
I/42.5R 375 kg
Admix u e—Rheobuild 1000 4.8 `
Silica Fume (Sikac e e HD) 41 kg
Wa e (A) 145 `
A/(C +Addi ions) 0.35
Appl. Sci. 2020,10, 642 5 o 14
The o dina y ein o cemen used in he beams consis ed o ho olled ibbed s eel ba s (wi h 10
and 16 mm diame e s) sold comme cially as Class A500. In o de o know he a e age alues o he
yield s ess and co esponding s ain o he ba s (
y
and
εy
, espec i ely), ensile es s on s eel samples
we e ca ied ou (6 samples o each o he diame e s ha we e used in he beams). The ollowing
a e age alues we e ob ained—
y=
686
MPa
and
εy=
3.43
×
10
−3
. Fo he s eel Young
´
s Modulus,
he ypical alue se in codes o p ac ice was assumed, Es=200 GPa [16].
As example, Figu e 4a illus a es some
σ–ε
cu es eco ded du ing he ensile es s o s eel
specimens (o dina y ein o cemen ).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 o 14
The o dina y ein o cemen used in he beams consis ed o ho olled ibbed s eel ba s (wi h 10
and 16 mm diame e s) sold comme cially as Class A500. In o de o know he a e age alues o he
yield s ess and co esponding s ain o he ba s (
y
and ε
y
, espec i ely), ensile es s on s eel
samples we e ca ied ou (6 samples o each o he diame e s ha we e used in he beams). The
ollowing a e age alues we e ob ained— 686 MPa=
y
and 3
ε3.4310
y
−
=×
. Fo he s eel Young´s
Modulus, he ypical alue se in codes o p ac ice was assumed,
200 GPa
s
E=
[16].
As example, Figu e 4a illus a es some
σ−ε
cu es eco ded du ing he ensile es s o s eel
specimens (o dina y ein o cemen ).
(a)
(b)
Figu e 4. Uniaxial
σ
–
ε
cu es o ein o cemen : (a) o dina y and (b) p es ess.
The p es ess ein o cemen used in Beams D-1.79 and D-3.08 consis ed o ou 0.6′′ wi es (0.6
inches o 1.52 cm diame e ) belonging o Class S1670/1860. Tes s on 6 p es ess wi e specimens we e
also ca ied ou and he a e age alues o he 0.1% limi p opo ional s ess (
0.1%p
) and he ul ima e
s ess (
pu
) o he wi es we e ob ained—
0.1%
1670.5 MPa=
p
and 1867.1 MPa=
pu
, espec i ely.
The co esponding s ain a 0.1% was compu ed by assuming a linea ela ionship be ween s ains
and s esses, which led o 3
0.1%
ε 8.567 10
p
−
=×
. The Young’s Modulus was assumed o be he one
indica ed by he supplie ,
195 GPa
p
E=.
As example, Figu e 4b illus a es σ−ε cu es eco ded du ing he ensile es o wo p es ess
s eel specimens (wi h 4 × 0.6 inches wi es each).
Figu e 4. Uniaxial σ–εcu es o ein o cemen : (a) o dina y and (b) p es ess.
The p es ess ein o cemen used in Beams D-1.79 and D-3.08 consis ed o ou 0.6
00
wi es (0.6
inches o 1.52 cm diame e ) belonging o Class S1670/1860. Tes s on 6 p es ess wi e specimens we e
also ca ied ou and he a e age alues o he 0.1% limi p opo ional s ess (
p0.1%
) and he ul ima e
s ess (
pu
) o he wi es we e ob ained—
p0.1% =
1670.5
MPa
and
pu =
1867.1
MPa
, espec i ely. The
co esponding s ain a 0.1% was compu ed by assuming a linea ela ionship be ween s ains and
s esses, which led o
εp0.1% =
8.567
×
10
−3
. The Young’s Modulus was assumed o be he one indica ed
by he supplie , Ep=195 GPa.
As example, Figu e 4b illus a es
σ–ε
cu es eco ded du ing he ensile es o wo p es ess s eel
specimens (wi h 4 ×0.6 inches wi es each).
I should be e e ed ha some slip was obse ed be ween he s eel specimens and he claws
o he es machine. This explains he appa en di e en ini ial s i ness be ween he cu es o 10

Appl. Sci. 2020,10, 642 6 o 14
and 16 mm ba s in Figu e 4a and also he ini ial pa o he cu es in Figu e 4b. This p oblem had no
implica ion o he p e iously p esen ed s ain alues a he end o he elas ic s age. The s ains we e
compu ed om Hooke’s law by knowing he s esses and assuming he Young’s Modulus.
2.3. Tes ing P ocedu e
The es de ice is made o h ee main componen s:
•a es ame whe e he mechanical ac ua o is ixed;
•
a de ice ha ecei es he load om he mechanical ac ua o and applies a o sional momen in
one end o he es beams;
•
a de ice ha ixes he es beam a he o he end, es ic ing i s ans e sal o a ion ( wis ) and
allowing i s longi udinal de o ma ion (elonga ion).
Figu e 5illus a es he global es de ice wi h a beam in i s es posi ion.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 o 14
I should be e e ed ha some slip was obse ed be ween he s eel specimens and he claws o
he es machine. This explains he appa en di e en ini ial s i ness be ween he cu es o 10 and
16 mm ba s in Figu e 4a and also he ini ial pa o he cu es in Figu e 4b. This p oblem had no
implica ion o he p e iously p esen ed s ain alues a he end o he elas ic s age. The s ains we e
compu ed om Hooke’s law by knowing he s esses and assuming he Young’s Modulus.
2.3. Tes ing P ocedu e
The es de ice is made o h ee main componen s:
• a es ame whe e he mechanical ac ua o is ixed;
• a de ice ha ecei es he load om he mechanical ac ua o and applies a o sional momen in
one end o he es beams;
• a de ice ha ixes he es beam a he o he end, es ic ing i s ans e sal o a ion ( wis ) and
allowing i s longi udinal de o ma ion (elonga ion).
Figu e 5 illus a es he global es de ice wi h a beam in i s es posi ion.
Figu e 5. Tes se up.
The load was applied by imposing a low de o ma ion a e wi h an elec omechanical ac ua o .
Se e al load cells we e placed in di e en poin s o he global es de ice in o de o eco d a any
ime he gene al loading s a e o he beams.
2.95
0.60
5.90
(applied o que)
To que machine
0.600.55 0.60 0.60
i
x : 0.55 1.15
BA
BA
PLAN VIEW
1.75
C
C
2.35
D
D
0.600.600.60 0.550.60
( es ained o que)
3.55
F
F
E
E
4.15
G
G
Beam specimen
5.35
I
I
4.75
H
H
5.90
J
J
Reac ion wall
LEFT LATERAL VIEW
Load a m
Applied load
0.85
LONGITUDINAL VIEW
LONGITUDINAL SECTION
Figu e 5. Tes se up.
The load was applied by imposing a low de o ma ion a e wi h an elec omechanical ac ua o .
Se e al load cells we e placed in di e en poin s o he global es de ice in o de o eco d a any ime
he gene al loading s a e o he beams.
The ans e sal o a ions ( wis s) we e ead in 10 sec ions uni o mly spaced along he leng h o
he beams (Sec ions A-A o J-J), as illus a ed in Figu e 5. Fo his, 10 pai s o displacemen ansduce s
Appl. Sci. 2020,10, 642 7 o 14
we e placed a he op ace o he beam ( hey we e ixed o an ex e nal ancho ed e e en ial). Special ca e
was aken o allow ee ho izon al ela i e mo emen s be ween he beams and he LVDT a ms. Because
o his, he ho izon al p ojec ion o he dis ance be ween pai s o ansduce s emained cons an du ing
he es and he o a ion angles a each sec ion could be easily compu ed om he ansduce s’ eadings.
The o sional ein o cemen ba s we e ins umen ed in h ee selec ed sec ions a qua e s o he
beams’ leng h. Resis ance s ain gauges we e s uck on he 4 longi udinal co ne ba s and on he
4 b anches o one s i up.
Fo Beams D-1.79 and D-3.08, in o de o e alua e he e ec i e longi udinal p es essing o ce
a e losses and also he changes in his o ce due o he applica ion o inc easing o que, a load cell
was placed be ween he head o he beam and he head o ancho age. Figu e 6illus a es longi udinal
cu s a he ends o he p es essed beams and shows he echnical solu ions adop ed o p es ess he
beams and o ead he p es ess o ce du ing he es s.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 o 14
The ans e sal o a ions ( wis s) we e ead in 10 sec ions uni o mly spaced along he leng h o
he beams (Sec ions A-A o J-J), as illus a ed in Figu e 5. Fo his, 10 pai s o displacemen
ansduce s we e placed a he op ace o he beam ( hey we e ixed o an ex e nal ancho ed
e e en ial). Special ca e was aken o allow ee ho izon al ela i e mo emen s be ween he beams
and he LVDT a ms. Because o his, he ho izon al p ojec ion o he dis ance be ween pai s o
ansduce s emained cons an du ing he es and he o a ion angles a each sec ion could be easily
compu ed om he ansduce s’ eadings.
The o sional ein o cemen ba s we e ins umen ed in h ee selec ed sec ions a qua e s o he
beams’ leng h. Resis ance s ain gauges we e s uck on he 4 longi udinal co ne ba s and on he 4
b anches o one s i up.
Fo Beams D-1.79 and D-3.08, in o de o e alua e he e ec i e longi udinal p es essing o ce
a e losses and also he changes in his o ce due o he applica ion o inc easing o que, a load cell
was placed be ween he head o he beam and he head o ancho age. Figu e 6 illus a es longi udinal
cu s a he ends o he p es essed beams and shows he echnical solu ions adop ed o p es ess he
beams and o ead he p es ess o ce du ing he es s.
Figu e 6. Ancho age zones a bo h ends o he p es essed beams.
A Da a Logge was used o eco d all he eadings. Figu e 7 shows gene al iews o a beam in
i s posi ion wi h he ins umen a ion eady o es ing.
Figu e 7. Beam specimen in es posi ion.
endon
s eel pla e
load cell
s eel ube
ancho age head
s eel pla e
ancho age head
endon
Figu e 6. Ancho age zones a bo h ends o he p es essed beams.
A Da a Logge was used o eco d all he eadings. Figu e 7shows gene al iews o a beam in i s
posi ion wi h he ins umen a ion eady o es ing.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 o 14
The ans e sal o a ions ( wis s) we e ead in 10 sec ions uni o mly spaced along he leng h o
he beams (Sec ions A-A o J-J), as illus a ed in Figu e 5. Fo his, 10 pai s o displacemen
ansduce s we e placed a he op ace o he beam ( hey we e ixed o an ex e nal ancho ed
e e en ial). Special ca e was aken o allow ee ho izon al ela i e mo emen s be ween he beams
and he LVDT a ms. Because o his, he ho izon al p ojec ion o he dis ance be ween pai s o
ansduce s emained cons an du ing he es and he o a ion angles a each sec ion could be easily
compu ed om he ansduce s’ eadings.
The o sional ein o cemen ba s we e ins umen ed in h ee selec ed sec ions a qua e s o he
beams’ leng h. Resis ance s ain gauges we e s uck on he 4 longi udinal co ne ba s and on he 4
b anches o one s i up.
Fo Beams D-1.79 and D-3.08, in o de o e alua e he e ec i e longi udinal p es essing o ce
a e losses and also he changes in his o ce due o he applica ion o inc easing o que, a load cell
was placed be ween he head o he beam and he head o ancho age. Figu e 6 illus a es longi udinal
cu s a he ends o he p es essed beams and shows he echnical solu ions adop ed o p es ess he
beams and o ead he p es ess o ce du ing he es s.
Figu e 6. Ancho age zones a bo h ends o he p es essed beams.
A Da a Logge was used o eco d all he eadings. Figu e 7 shows gene al iews o a beam in
i s posi ion wi h he ins umen a ion eady o es ing.
Figu e 7. Beam specimen in es posi ion.
endon
s eel pla e
load cell
s eel ube
ancho age head
s eel pla e
ancho age head
endon
Figu e 7. Beam specimen in es posi ion.
Appl. Sci. 2020,10, 642 8 o 14
3. Global Analysis o he Expe imen al Resul s
3.1. To sional Momen s s. Twis s
Figu e 8p esen s he g aphs o o que (
T
) e sus he a e age wis s (
θm
) o he es ed beams.
The o que,
T
, was ob ained mul iplying he load applied by he ac ua o by he ho izon al p ojec ion
o he le el a m, 0.85
m
, which emained cons an (see Figu e 5). The a e age wis ,
θm
, was ob ained
by di iding he expe imen al angle measu ed in Sec ion A-A o he dis ance be ween Sec ions A-A
and J-J, 5.35
m
(Figu e 5). In each
T–θm
cu e, iden i ica ion ma ks we e used o highligh he poin s
co esponding o c acking () and o yielding o he ans e se () and longi udinal (4) ein o cemen .
The yielding poin s we e calcula ed om he expe imen al alues o he s ains eco ded by he s ain
gauges s uck o he ein o cemen ba s.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 o 14
3. Global Analysis o he Expe imen al Resul s
3.1. To sional Momen s s. Twis s
Figu e 8 p esen s he g aphs o o que (T) e sus he a e age wis s ( θm) o he es ed beams.
The o que, T, was ob ained mul iplying he load applied by he ac ua o by he ho izon al
p ojec ion o he le el a m, 0.85 m, which emained cons an (see Figu e 5). The a e age wis , θm,
was ob ained by di iding he expe imen al angle measu ed in Sec ion A-A o he dis ance be ween
Sec ions A-A and J-J, 5.35 m (Figu e 5). In each θ−m
T cu e, iden i ica ion ma ks we e used o
highligh he poin s co esponding o c acking ( ) and o yielding o he ans e se ( ) and
longi udinal () ein o cemen . The yielding poin s we e calcula ed om he expe imen al alues o
he s ains eco ded by he s ain gauges s uck o he ein o cemen ba s.
Figu e 8. θ−m
T cu es.
As expec ed, Figu e 8 shows he high in luence o p es ess in he c acking o que. I is known
ha p es ess delays he o ma ion o c acking. Fo a mode a e conc e e s ess (induced by p es ess)
o 1.79 MPa (Beam D-1.79) an inc ease o app oxima ely 32.5% on he c acking o que is
obse ed, when compa ed wi h he beam wi hou p es ess (Beam D-0). This shows he e iciency o
uni o m longi udinal p es ess o delay he c acking in beams unde o sion. This high in luence o
p es ess can be explained because in o sion he conc e e is unde a lowe and mo e uni o m le el
o ensile s esses (in he whole sec ion) when compa ed wi h he bending si ua ion. The e o e, e en
o low le els o p es ess, he c acking s age is delayed. I is also obse ed ha , in S a e I (non-c acked
s a e), he s eel ba s, including he p es essed wi es, gene ally ha e li le in luence on he s i ness o
he beams. In ac , he θ−m
T cu es a e almos coinciden a his s a e.
In S a e II (c acked s a e), he θ−m
T cu es a e almos pa allel o each o he . This shows ha
he con ibu ion o he longi udinal p es ess o he s i ness o he beams is small a his s a e. This
is due o he adop ed p es essing echnique (ex e nal longi udinal and cen ed p es ess).
As expec ed, Figu e 8 also shows ha he use o p es ess inc eases he esis an o que,
T, o
he beams. Howe e , he e is no a clea endency wi h espec o he associa ed wis a he ul ima e
o que, θ
T. In ac , since p es ess induces a comp essi e s ess s a e in conc e e, i would be
expec ed ha he de o ma ion capaci y o conc e e in he comp essed a eas o he beam (namely in
he s u s) would dec ease as he le el o p es ess inc eases. As a consequence, he wis
co esponding o he ul ima e o que should dec ease as he s ess induced by p es ess inc eases.
This is no he case o Beam D-3.08, which has he highes le el o p es ess and eaches a wis θ
T
0
100
200
300
400
500
0.0 0.5 1.0 1.5 2.0 2.5
T(kNm)
θ
m
(º/m)
D-1.79
D-3.08
D-0
C acking
Yielding As
Yielding Asl
Figu e 8. T–θmcu es.
As expec ed, Figu e 8shows he high in luence o p es ess in he c acking o que. I is known
ha p es ess delays he o ma ion o c acking. Fo a mode a e conc e e s ess (induced by p es ess)
o 1.79
MPa
(Beam D-1.79) an inc ease o app oxima ely 32.5% on he c acking o que is obse ed,
when compa ed wi h he beam wi hou p es ess (Beam D-0). This shows he e iciency o uni o m
longi udinal p es ess o delay he c acking in beams unde o sion. This high in luence o p es ess
can be explained because in o sion he conc e e is unde a lowe and mo e uni o m le el o ensile
s esses (in he whole sec ion) when compa ed wi h he bending si ua ion. The e o e, e en o low
le els o p es ess, he c acking s age is delayed. I is also obse ed ha , in S a e I (non-c acked s a e),
he s eel ba s, including he p es essed wi es, gene ally ha e li le in luence on he s i ness o he
beams. In ac , he T–θmcu es a e almos coinciden a his s a e.
In S a e II (c acked s a e), he
T–θm
cu es a e almos pa allel o each o he . This shows ha he
con ibu ion o he longi udinal p es ess o he s i ness o he beams is small a his s a e. This is due
o he adop ed p es essing echnique (ex e nal longi udinal and cen ed p es ess).
As expec ed, Figu e 8also shows ha he use o p es ess inc eases he esis an o que,
T
, o
he beams. Howe e , he e is no a clea endency wi h espec o he associa ed wis a he ul ima e
o que,
θT
. In ac , since p es ess induces a comp essi e s ess s a e in conc e e, i would be expec ed
ha he de o ma ion capaci y o conc e e in he comp essed a eas o he beam (namely in he s u s)
would dec ease as he le el o p es ess inc eases. As a consequence, he wis co esponding o he
ul ima e o que should dec ease as he s ess induced by p es ess inc eases. This is no he case o
Beam D-3.08, which has he highes le el o p es ess and eaches a wis
θT
ha exceeds he same one
o he o he beams. Howe e , his obse a ion can be explained due o he ype o ailu e o Beams D-0
and D-1.79, which was agile and somehow p ema u e ( ailu e by pull o o he conc e e co ne s).
Appl. Sci. 2020,10, 642 9 o 14
This subjec will be discussed la e . This aspec also jus i ies he di e en shape o he descending
b anches o
T–θm
cu es ha is obse ed and he absence o yielding poin s be o e he peak o que is
eached o Beam D-0.
T–θm
cu es o Figu e 8also show ha , be o e he peak o que is eached, he p es essed beams
only p esen poin s co esponding o yielding o he ans e se ein o cemen . I is obse ed ha
he yielding o longi udinal ein o cemen only occu s a e he peak o que. A e c acking, he
longi udinal p es ess ein o cemen s a s wo king as o dina y ein o cemen unde he o sional
loading. Consequen ly, he beams wi h balanced longi udinal o ans e se ein o cemen a ios will
lose his balance because o he in luence o he p es ess wi es. Hence, he calcula ion o he balanced
a io o he longi udinal o ans e se ein o cemen s should accoun o he a ea o he p es essed s eel
(
mb, o = (Asl +nAsp)s/As u
wi h
n=Ep/Es
), which leads o an excess o longi udinal ein o cemen o
abou 20%. The e o e, he ans e se ein o cemen should yield be o e he longi udinal ein o cemen ,
as obse ed in Figu e 8.
Table 3p esen s, o each es ed beam, he main p ope ies o
T–θm
cu es, namely— he c acking
o que and co esponden wis (
Tc
and
θc
), he o sional s i ness in S a e I (
(GC)I
), he o sional
s i ness in S a e II (
(GC)II
), he o que co esponding o he yielding o he ans e se ein o cemen
and co esponden wis (
T y
and
θ y
), he esis an o que (peak o que) and co esponden wis
(
T
and
θT
). Since he yielding o he longi udinal ein o cemen occu s a e he peak o que, he
co esponding alues a e no p esen ed.
Table 3. P ope ies o T–θmcu es.
Beam Tc
kNm θc ◦/m(GC)I
kNm2TII=aθII+b(GC)II
kNm2
T y
kNm θ y ◦/mT kNm θT
◦/m
D-0 130.5 0.04 172,940 a=170.87; b=119.43 9790 - - 355.9 1.45
D-1.79 172.9 0.07 152,188 a=194.73; b=142.95 11,157 314.9 0.87 396.0 1.38
D-3.08 184.7 0.08 141,823 a=148.05; b=132.34 14,212 430.0 1.34 447.7 1.57
The o sional s i ness in S a e I was calcula ed di iding
Tc
by
θc
(wi h
θc
in adians uni ). P io
o he calcula ion o he o sional s i ness in S a e II, he equa ion o he line o
T–θm
cu e in he linea
elas ic s age was p e iously calcula ed om linea in e pola ion. Fo his calcula ion, he poin s o he
T–θm
cu es loca ed in he zone ha can be iden i ied as belonging o S a e II we e selec ed. Only he
zone o he cu es ha is app oxima ely a s aigh line was conside ed. A e he calcula ion o he
equa ion,
T=aθ+b
(see Table 3), he s i ness
(GC)II
is equal o he slope
a
o he line (wi h wis s
con e ed o adian uni s).
The analysis o he alues displayed in Table 3con i ms he ends obse ed in he
T–θm
cu es
om Figu e 8and p e iously discussed.
3.2. Fo ce in he P es ess Rein o cemen s. Twis s
Figu e 9p esen s he g aphs o he o ce in he longi udinal p es ess ein o cemen (
Fps
) e sus
he a e age wis (
θm
). The o ce
Fps
was ob ained di ec ly om he load cell placed in he ancho age
zone o he p es essed wi es. The e olu ion o he eco ded alues s a s om he ini ial alue o he
applied p es ess o ce (a e sho - e m losses).
The cu es o Figu e 9show he exis ence o a small ho izon al zone whe e he o ce in he
p es ess ein o cemen is almos cons an and equal o he o ce due o ini ial p es ess. This zone
ends as he i s c ack appea s in he beam. A e his zone, he o ce in he p es essed wi es inc eases
g adually. In ac , be o e c acking, he in e nal ein o cemen s eel ba s a e also unde e y low le els
o s ess. The s ains in he beam du ing he p e-c acking s a e a e e y small, as con i med by he
eadings o he s ains in he ein o cemen ba s ( eco ded om he s ain gauges). Decomp ession o
conc e e akes place a a ce ain poin o his ini ial ho izon al zone (be o e his poin , conc e e is only
in comp ession).