Optimum Design of Vertical Steel Tendons Profile Layout of Post-Tensioning Concrete Bridges: Fem Static Analysis

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Optimum design of vertical steel tendons proﬁle layout of post-tensioning

concrete bridges: Fem static analysis
Article · December 2018
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VOL. 13, NO. 23, DECEMBER 2018 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2018 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
OPTIMUM DESIGN OF VERTICAL STEEL TENDONS PROFILE LAYOUT

OF POST-TENSIONING CONCRETE BRIDGES: FEM STATIC ANALYSIS
Ali Fadhil Naser
Department of Building and Construction Engineering, Al-Mussaib Technical College, Al-Furat Al-Awsat Technical University,
Babylon, Iraq
E-Mail: ali_hu73@yahoo.com
ABSTRACT
The objectives of this study are to evaluate the optimum design of tendon profile layout, to study the effect of
tendon profile layout on the structural performance of post-tensioned concrete bridge model, and to investigate the
locations effect of anchorages points of tendons on the vertical deflection. There were four factors were selected such as
bending moment, shear force, stress, and vertical deflection. According to supports of tendons, there are two cases of
bridges models. The first case is used simply-supported tendons profile layout. The second case is adopted continuous
tendons profile layout. According to profile layout of tendons, the first case consists of seven bridge models (7-Models)
and the second case includes ten bridge models (10-Models). The results of FEM analysis showed that the tendon profile
layout had important effect on the structural performance of post-tensioned concrete bridges according to types and
number of anchorages points of tendons. For pre-stressed load stage, simply-supported tendon profile model appeared
maximum value of upward vertical deflection (3mm) was more than continuous tendon model (2mm). The maximum
downward vertical deflection is 12mm within continuous tendon model which is less than value of simply-supported
tendon model (13mm). According to service load stage analysis, continuous tendon model had the minimum value of
downward vertical deflection (14mm) was more than simply-supported tendon model (15mm), but maximum value of
downward vertical deflection was appeared in simply-supported tendon model (27mm) was more than the maximum value
of downward vertical deflection (26mm) within continuous tendon model. It can be concluded that continuous tendon
profile model was convenient for design of post-tensioned concrete bridge because it can be resisted service loads and had
the lower value of vertical deflection.
Keywords: post-tensioned, tendon, bridge model, profile layout, vertical deflection, bending moment, shear force, stress.
1. INTRODUCTION quicker construction, reduced cost, and design flexibility.

A bridge is a significant and competent structure The components of post-tensioned system include wires,
and it involves of numeral of components. These strands, ducts, and tendons and corrosion protection
components include two parts. First parts are including the equipment. The single wire has diameter which is 0.2 inch
bearings, girders or beams, deck, joints, pavement layers, and it made of high-strength steel meeting ASTM A416
security barrier, and drainage system. They were known as specifications. Strand has seven wires with a nominal
superstructure. While, the second parts were known as diameter of 0.6 inches. Tendons are containing a group of
substructure which was consisted of the foundations, piers, several strands (structural load-carrying elements) and the
and pier caps. Bridge structure can be constructed over an cementations grout and duct (non-structural, corrosion-
obstruction, such as rivers, highways, railways. Bridges protection elements). Tendons can be classified as bonded
structures can be classified according to materials and and un-bonded tendons. Bonded tendon can be defined as
types of supports. According materials of construction, the direct contact or bonded to the adjacent concrete.
types of bridges include concrete bridges, pre-stressed Whereas, un-bonded tendons is not in direct contact with
concrete bridges, wood bridges, and steel bridges. For concrete or cannot transfer the stress through the surface
types of supports, the bridges structures include simply bonding. [9, 10, 11].
supported bridges and continues bridges [1, 2, 3, 4]. The strength of tendons depends on the durability
The system of pre-stressed concrete bridge deals of the system materials such as pre-stressed steels,
with the applied of tendons loads before the application of anchorages, ducts, grouted materials, the setting up of
the service loads (traffic loads, dead load, temperature these materials, and design concept specifics. The post-
load, wind load, and live load) on the bridge structure. Pre- tensioning layout and layers of protection such as concrete
stressed concrete system consists of two types. The first cover and selected materials in view of the aggressively of
type is pre-tensioning. The second type is post-tensioning. the environment for instance [12].
Post-tensioning is a method of concrete structure The layout of tendons profile shows an important
reinforcement with high strength steel strand or bars character in the decreasing of tension stress from concrete.
referred to as tendons [5, 6, 7, 8]. The curvature degree of tendons applies force on the
Post-tensioned concrete system is widely used in concrete to balance the forces that causing tension stresses.
the erection of bridges structures because this system The tendons are located with eccentricities towards the
provides several advantages over normal reinforcement soffit of the beam to stabilize the sagging bending
concrete. Also it contains on more efficient use of moments due to crosswise loads. Therefore, the pre-
materials, better deflection and crack control, durability, stressed concrete beams bend upwards (camber) on the
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application of pre-stressed load. The tendons profile will a two-way pre-stressed concrete slab has been successfully
represent the shape of the bending moment diagram when designed considering several design criteria. [16]
the bending moment is the product of the pre-stressed load C. Kumar and L. Venkat (2013) used the genetic
and eccentricity [13]. algorithm based optimum design of pre-stressed concrete
The main objectives of this research are to beams. Their paper deals with the optimization of a simply
evaluate the optimum design of tendon profile layout, to supported pre-stressed beam subjected to live and dead
study the effect of tendon profile layout on the structural loads using genetic algorithm method. They studied the
performance of post-tensioned concrete bridge model, and cost of tendons and concrete. They were taken cost ratio of
to investigate the locations effect of anchorages points of tendons to concrete is taken as 8. They considered
tendons on the vertical deflection. different factors in the analysis. These factors are the
effect of beam length on optimum cost, effect of profile of
2. RELATED PAST STUDIES tendons on optimum cost, effect of population size on cost
The tendon profile layout is important factor in ratio, effect of live load on optimum cost. The results of
the design of post- tensioning concrete bridges but most analysis showed that the percentage difference in optimum
studies that deal with tendons profile layout were studied cost between 14m and 15m of beam length is 21.7%. The
the effects of them on the structural performance for percentage difference in optimum cost between 50kN/m to
simply normal concrete beams and concrete slab. 60kN/m of live load is 16.8%. For length of beam is 13m,
Therefore, the present paper will be focused on the there is not effect of restraining the tendons profile, but for
tendons profile layout design for post-tensioning concrete 14m and 15m of beam lengths, parabolic tendons profile
bridges (simply-supported bridges and continuous gives higher optimum cost as compared to straight tendons
bridges). profile. The percentage increase in optimum cost is 4.22%
P. Ng and A. Kwan (2006) noted that the for the parabolic tendon profile when compare to straight
determination of pre-stressed tendon profile is a critical tendon profile [17].
stage in the design of post-tensioning concrete structures. P. Colajania et al (2013) explained the design
They explained that the load-balancing method provides procedure for pre-stressed concrete beams. they provided
great probable for direct determination of tendon profile. the optimal layout of ordinary reinforcement in pre-
They used load-balancing method with different stressed concrete beams that subjected to bending moment
considerations in the application of this method and they and shear force. [18]
presented two examples to explain the step-by-step A. Dixit and V. Khurd (2017), developed three-
procedures. The results shown that the method is dimensional finite element modeling of post-tensioning
essentially simple to appliance, even in complicated concrete beam that can be used to investigate the effect of
structures like curved continuous bridges. Finally, they eccentricity, pre-stressed load and tendons profile for
concluded that the load-balancing method is a much more concentrated point loading. They used ANSYS program in
efficient alternative to the conventional method and should analysis. The results of static analysis showed that the
be incorporated in the standard design process. [14] eccentricity, pre-stressed load and tendons profile are
A. Ali et al (2010) presented the tendons layout important factors and they should be taken into
design of one-way pre-stressed concrete slabs using finite consideration while designing the post-tensioning concrete
element method analysis. They used B-Spline method for beam. [19]
tendons layout design of pre-stressed concrete slabs. The K. Abdul-Razzaq et al (2018) investigated the
stresses in the structure were calculated by using finite structural performance of post-tensioned two-way concrete
element method. They stated that the method of modeling slabs. with the different bonded tendons layout. They used
tendons as parabola and variable their eccentricities to non-linear finite element analysis method to select the
decrease tension stresses of the concrete lags behind most active and optimum location of tendons layout with
because of the tendons are not truly parabolic especially in different number of tendons and applied load on the
continuous structures. The shape of tendons was changed concrete two-way slab. They found that the results of
to get the desired profile by varying the ordinates of the B- analysis showed that the failure load in post-tensioning in
spline. The tendons layout is developed so that stresses in both directions increased about 89 % as compared with
the structural element be below the limiting tensile stress. slab post-tensioning in one direction. [20]
According to stresses results of finite element analysis,
tendons profile was changed in iterative manner [15]. 3. BRIDGES MODELS DETAILS
A. Ali et al (2013) presented a new method to In the present paper, continuous box girder post-
design tendons layout of pre-stressed concrete slabs. They tensioned concrete bridge model is selected. There are two
were using B-spline to model and account the tendons cases of bridges models according to supports of tendons.
profile perfectly. They developed efficient algorithm to The first case is used simply-supported tendons profile
obtain the tendons layout for pre-stressed concrete slabs. layout (the start anchorage and end anchorage of tendons
According to finite element computations, tendon and along each span). The second case is adopted continuous
concrete are modeled by using 3 nodes of bar and 20 tendons profile layout (the start anchorage and end
nodes of brick elements respectively. The tendon- concrete anchorage of tendons along all spans). According to
interactions are precisely accounted using vector calculus profile layout of tendons, the first case consists of seven
formulae. They found that the using of proposed technique bridge models (7-Models) and the second case includes
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ten bridge models (10-Models). The length of continuous models. Figure-1 shows the longitudinal and transverse
box girder post-tensioned concrete bridge is 80m with four bridge model. Table-1 lists the bridge models with profile
spans (each span length is 20m) and the width is equal to layout for case 1. Table-2 lists the bridge models with
11m. the load of pre-stressing tendon is same foe all profile layout for case 1.
(a) (b)
Figure-1. The bridge model: (a) longitudinal section, (b) transverse section.
Table-1. The bridge models with profile layout for case 1.
Model no. Profile name Layout
Model No. 1 Straight tendon
Model No. 2 Straight tendon with two bends
Model No. 3 Straight tendon with three bends
Parabolic tendon with two concave

Model No. 4
bends
Parabolic tendon with two convex
Model No. 5
bends
Parabolic tendon with two points
Model No. 6
(down-up)
Parabolic tendon with two points
Model No. 7
(upward)
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Table-2. Profile tendon layout for case 2.
Model No. Profile name Layout

Model No. 1 Straight tendon
Model No. 2 Straight tendon with four bends in all spans
Model No. 3 Straight tendon with two bends in all spans
Model No. 4 Straight tendon with six bends in all spans
Model No. 5 Straight tendon with three bends in all spans
Model No. 6 Parabolic tendon with four concave bends in all spans
Model No. 7 Parabolic tendon with two concave bends in all spans
Model No. 8 Parabolic tendon with two convex bends in all spans
Model No. 9 Parabolic tendon (down-up) in all spans
Model No. 10 Parabolic tendon (upward) in all spans
4. RESULTS OF FEM ANALYSIS bending moment (33630kN.m) and the maximum value of
Tendons profile layout is an important factor that positive bending moment is 42204kN.m. within model
is effected the static behavior of post-tensioned concrete No.7. For shear force, model No. 5 show the higher values
bridges. Sap2000 program is used in the FE Analysis of of positive and negative shear force which is 12154kN and
bridges models. Static analysis is adopted to evaluate the 11843kN respectively. Maximum tensile stress appears in
optimum design of tendons profile layout. The FE model No.6 and No. 1(7.17MPa), thus these models will
Analysis is used to calculate the positive and negative have more cracks. The maximum compressive stress is
bending moment, shear force, tensile and compressive 10.98Mpa in model No.7. Model No.3 shows the
stresses, and vertical deflection. There are two stages of maximum value of upward deflection which is 3mm and
internal design loads for each case of analysis. These model No.5 gives maximum value of downward deflection
stages are pre-stressed load and service loads (13mm). According to above results of pre-stressed load
(combinations of loads). analysis for simply-supported tendons profile layout (case
1); model No.3 (straight tendon with three bends) is
4.1 FEM analysis of simply-supported tendons suitable for design because it shows upward vertical
profile layout (case 1) deflection more than others models. Models No.5 and
No.6 are not suitable for design because of they appear
4.1.1 Pre-stressed load stage maximum values of positive bending moment, shear force,
The results of pre-stressed load stage for case 1 and downward vertical deflection. Figure-2 shows the
show that model No. 6 gives maximum value of positive results of pre-stressed load stage fore case 1.
(a)
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(b)
(c)
(d)
Figure-2. Results of pre-stressed load stage fore case 1: (a) bending moments,
(b) shear forces, (c) stresses, (d) vertical deflection.
4.1.2 Service load stage within model No.7. Model No. 6 gives the maximum
Figure-3 explains the results of service load stage value of compressive stress and model No. 7 shows
analysis for case 1. From this Figure it can be seen that the maximum value of tensile stress. The higher value of
minimum value of downward deflection is 15mm within positive and negative shear force is 24724kN and
model No. 3 and No.4, and maximum value is 27mm 23317kN within model No.5 respectively. Model No.7
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shows the maximum positive bending moment concluded that model No. 3 (straight tendon with three
(60590kN.m) and Model No. 6 shows maximum negative bends) is more convenient from others models in the
bending moment (81892kN.m). From analysis, it can be design of tendon profile layout.
(a)
(b)
(c)
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(d)
Figure-3. Results of service load stage analysis for case 1: (a) bending moments,
(b) shear forces, (c) stresses, (d) vertical deflection
4.2 FEM Analysis of continuous tendons profile 4.2.2 Service load stage
layout (case 2) Service load stage represents the application of
all loads (combinations of all types of loads) in the
4.2.1 Pre-stressed load stage analysis of bridge structures models. The analysis results
The results of pre-stressed load stage can be seen of this stage shows that the minimum value of downward
that in Figure-4. This figure shows that the maximum vertical deflection is 14mm within models No. 4 and No.6.
upward vertical deflection appears in models No. 2, No. 4, Therefore, these models have good opportunity to use in
No. 6 which is 2mm. These models also have smaller the design of tendon profile layout more than others
values of downward vertical deflection. Therefore, these models. Model No. 9 shows the maximum value of
models are more convenient to design of tendon profile downward vertical deflection (26mm). The higher and
layout according to vertical deflection evaluation because lower values of tensile stress is 10.94MPa and 4.39MPa in
of the pre-stressed loads can be resisted the total loads of model No. 9 and No.6 respectively. So model No. 9 will
bridge structure. The maximum downward vertical have more cracks than others models. For compressive
deflection shows within model No. 10 and it is 12mm. stress, model No. 3 gives the maximum value which is
indicating that pre-stressed load cannot carry the load of 15.58MPa and the lower value is 8.85MPa in model No. 4.
bridge structure. Model No. 8 gives the lower value of The maximum positive and negative shear force is
tensile stress (1.64MPa) and the higher value of tensile 18116kN and 16929kN within model No.9 and No.8
stress is 6.41MPa in model No.7. Therefore, the cracks respectively. The maximum positive and negative bending
will be appeared in this model. The maximum positive and moment is 56444kN.m and 58376kN.m in model No.9.
negative shear force is 6642kN and 6637kN respectively Figure-5 shows the analysis results of service load stage
within model No.6. Model No.10 shows the maximum for case 2.
positive bending moment (34393kN.m) and Model No. 9
shows maximum negative bending moment (18671kN.m).
9250
(a)
(b)
(c)
9251
(d)
Figure-4. Analysis results of pre-stressed load stage for case 2: (a) bending moments,
(a)
(b)
9252
(c)
(d)
Figure-5. Analysis results of service load stage for case 2: (a) bending moments,
5. COMPARISON OF PRE-STRESSED AND simply-supported tendon model (13mm). According to

SERVICE LOAD STAGES service load stage analysis, continuous tendon model had
To compare between simply-supported and the minimum value of downward vertical deflection
continuous tendon profile layout, upward and downward (14mm) was more than simply-supported tendon model
vertical deflection values are selected. For pre-stressed (15mm), but maximum value of downward vertical
load stage, simply-supported tendon model appeared deflection was appeared in simply-supported tendon
maximum value of upward vertical deflection (3mm) was model (27mm) was more than the maximum value of
more than continuous tendon model (2mm). The downward vertical deflection (26mm) within continuous
maximum downward vertical deflection is 12mm within tendon model. Figure-6 shows the comparison results for
continuous tendon model which is less than value of case 1. Figure-7 shows the comparison results for case 2.
9253
Figure-6. The comparison results for case 1.
Figure-7. The comparison results for case 2.
6. CONCLUSIONS deflection more than others models. Models No.5 and

a) Continuous box girder post-tensioned concrete No.6 are not suitable for design because of they appear
bridge model is selected to evaluate the optimum design of maximum values of positive bending moment, shear force,
tendon profile layout. According to supports of tendons and downward vertical deflection. The minimum value of
anchorages, there are two cases of bridges models. The downward deflection is 15mm within model No. 3 and
first case is used simply-supported tendons profile layout No.4, and maximum value is 27mm within model No.7.
(the start anchorage and end anchorage of tendons along Therefore, it can be concluded that model No. 3 (straight
each span). The second case is adopted continuous tendons tendon with three bends) is more convenient from others
profile layout (the start anchorage and end anchorage of models in the design of tendon profile layout.
tendons along all spans). According to profile layout of c) The results of pre-stressed load stage for
tendons, the first case consists of seven bridge models (7- continuous tendon profile model showed that the
Models) and the second case includes ten bridge models maximum upward vertical deflection appears in models
(10-Models). No. 2, No. 4, No. 6 which is 2mm. These models also have
b) According to results of pre-stressed load stage smaller values of downward vertical deflection. Therefore,
analysis for simply-supported tendons profile layout (case these models are more convenient to design of tendon
1), model No.3 (straight tendon with three bends) is profile layout according to vertical deflection evaluation
suitable for design because it shows upward vertical because of the pre-stressed loads can be resisted the total
9254
loads of bridge structure. The maximum downward ARPN Journal of Engineering and Applied Sciences.
vertical deflection shows within model No. 10 and it is 5(11): 60-69.
12mm. indicating that pre-stressed load cannot carry the
load of bridge structure. Model No. 7, No.6, No.9 give the [7] PCI. 1968. Fundamentals of Pre-Stressed Concrete
higher value of tensile stress, the maximum positive and Design. Second Edition. Pre-Stressed Concrete
negative shear force, the maximum positive bending
Institute, Chicago, USA.
moment, and maximum negative bending moment
respectively.
[8] A. F. Naser and W. Z. Lin. 2013. Finite Element and
d) The analysis results of service load stages for
continuous tendon profile model explained that the Experimental Analysis and Evaluation of Static and
minimum value of downward vertical deflection is 14mm Dynamic Responses of Oblique Pre-stressed Concrete
within models No. 4 and No.6. Therefore, these models Box Girder Bridge. Research Journal of Applied
have good opportunity to use in the design of tendon Sciences, Engineering and Technology. 6(19): 3642-
profile layout more than others models. Model No. 9 3657.
shows the maximum value of downward vertical
deflection (26mm). The higher and lower value of tensile [9] A. Abdullah, A. Jennifer, H. Hamilton, G.
stress is appeared in model No. 9 and No.6 respectively. Consolazio. 2015. Damage Identification in Un-
For compressive stress, model No. 3 gives the
maximum value which is 15.58MPa and the lower value is bonded Tendons for Post-tensioned Bridges. 6th
8.85MPa in model No. 4. The maximum positive and International Conference on Advances in
negative shear force is 18116kN and 16929kN within Experimental Structural Engineering, University of
model No.9 and No.8 respectively. The maximum positive Illinois, Urbana-Champaign, USA.
and negative bending moment is 56444kN.m and
58376kN.m in model No.9. [10] D. Trejo, M. Beth, P. G. Radhakrishna. 2009. Effect
of Voids in Grouted, Post-Tensioned Concrete Bridge
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Optimum design of vertical steel tendons proﬁle layout of post-tensioning

Article · December 2018

Assist. Prof. Dr.Ali Fadhil Naser

EXPLORE THE BEST AND OFFER IT View project

Application of External Prestressing Tendons in the strengthening of bridges View project

The user has requested enhancement of the downloaded file.

OPTIMUM DESIGN OF VERTICAL STEEL TENDONS PROFILE LAYOUT

1. INTRODUCTION quicker construction, reduced cost, and design flexibility.

Table-1. The bridge models with profile layout for case 1.

Model no. Profile name Layout

Model No. 1 Straight tendon

Model No. 2 Straight tendon with two bends

Model No. 3 Straight tendon with three bends

Parabolic tendon with two concave

Table-2. Profile tendon layout for case 2.

Model No. Profile name Layout

Model No. 9 Parabolic tendon (down-up) in all spans

Model No. 10 Parabolic tendon (upward) in all spans

5. COMPARISON OF PRE-STRESSED AND simply-supported tendon model (13mm). According to

Figure-6. The comparison results for case 1.

Figure-7. The comparison results for case 2.

6. CONCLUSIONS deflection more than others models. Models No.5 and

[16] A. Ali, K. Pathak, N. Dindorkar. 2013. Cable Layout

[17] C. Kumar and L. Venkat. 2013. Genetic Algorithm

[18] P. Colajania, A. Recuperob and N. Spinella. 2013.

[19] A. Dixit and V. Khurd. 2017. Effect of Pre-stressing

[20] K. Abdul-Razzaq, A. Mohammed, T. Mohammedali.

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