CHALLENGE JOURNAL OF STRUCTURAL MECHANICS 5 (2) (2019) 62–71

Research Article

Structural analysis of reinforced concrete mansard roof structures

according to different structural plans

H. Selim Şengel a,* , İsmail Kanber b , Serdar Çarbaş c

a
Department of Civil Engineering, Eskişehir Osmangazi University, 26480 Eskişehir, Turkey
b
Graduate School of Natural and Applied Sciences, Eskişehir Osmangazi University, 26480 Eskişehir, Turkey
c
Department of Civil Engineering, Karamanoğlu Mehmetbey University, 70100 Karaman, Turkey

ABSTRACT ARTICLE INFO

In this study, analysis and evaluations were carried in order to determine the optimum condi- Article history:
tions of reinforced concrete mansard roof applications. In total 96 mansard and 24 non mansard
Received 27 March 2019
structure analysis were performed. The constructed models are symmetrical from all directions
Revised 16 May 2019
and it is modeled under the minimum conditions allowed by the regulation. As the column span,
the distance between the columns was determined as 4 meters. The span conditions were de- Accepted 22 May 2019
termined as 3 spans, 4 spans, 5 spans and 6 spans by evaluating the parcel sizes and zoning Keywords:
conditions. Thus, a total of 120 calculation models were created. The base shear force, column
Mansard roof
moments and the maximum top displacement values were discussed in concordance with these
calculations. As a result of the analysis, the graphical values of the mansard buildings were ex- Reinforced concrete
amined along with the non mansard buildings from the 3rd floor to the 8th floor, according to Span
the zoning plan. In this study, graphs of parcels, span values and the number of storeys were Estimate
drawn by keeping the values constant, and evaluations were made on the same graphs with and Displacement
non mansard. In addition, by looking at the movements of the graphs obtained from this study
on the same series, equations were adapted to the graphs and the series created with these
equations were expanded and stochastic parabolic cones were formed at the shear force for 10
storeys, in the column moments. The mean values for the top displacement chart were taken
and when the 20-storey displacement value was placed on this curve, it was determined that it
appeared at a point very close to the estimating equation curve. Based on the analysis results,
it is understood that it is possible to create a set of estimations for different number of storeys
and plans.

1. Introduction 8 storeys, buildings. When the Urban Development Plan

of Eskişehir province was examined, it was determined
Mansard roof is often applied to facilitate the use of that there were 3 different parcel types in use. These are
the inter-roof without increasing the number of storeys. adjacent parcels, corner parcels and discrete parcels.
Roofs in Turkey generally are discarded, unused spaces. According to the license data in Eskişehir province,
Mansard roof, however, provides an aesthetic form for 77% of the buildings in 2017 were manufactured as re-
these idle areas and creates areas of use (Üstün and inforced concrete. The applications of Mansard roofs in
Kolsal, 2016). Mansard roofs are constructed using Eskişehir are 95% reinforced concrete and 5% of them
wood and steel all around the world, however since are constructed as steel. In this study, the most appropri-
2014, an intensive reinforced concrete mansard roof ap- ate solutions for mansard roof are investigated and the
plication has been carried out in Eskişehir. data obtained from mansard roof solution results are
In this study, mansard roof reinforced concrete build- aimed to create prediction model graphs. While creating
ings located inside the provincial border of Eskişehir were these models, storey change and mold plans were cre-
examined in accordance with the license information and ated. 4 meters between the axes were preferred in order
it was determined that mansards in the region were to produce suitable spaces from the specified pattern
mostly 3 storeys, 4 storeys, 5 storeys, 6 storeys, 7 storeys, plans. The pattern plans are composed of 3, 4, 5 and 6

* Corresponding author. Tel.: +90-222-239-3750 ; Fax: +90-222-229-0535 ; E-mail address: ssengel@ogu.edu.tr (H. S. Şengel)
ISSN: 2149-8024 / DOI: https://doi.org/10.20528/cjsmec.2019.02.003
 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71 63

spans, respectively. In this study, the entire mansard 5, 6, 7 and 8. In addition, analysis models for estimation
roof and structural material were preferred as rein- charts were also drawn for 10 storeys and 20 storeys.
forced concrete material. The variables determined in
the model are the type of parcels, the number of storeys, 2.1. Schematic representation of Mansard roof
the number of spans in the mold plan, and in this way, a structures to be examined in accordance with the
total of 96 mansard and 24 non mansard model analysis parcels in Eskişehir
were created.
In this study, the mansard roof application infor- When the building regulations of the buildings in
mation in Eskişehir was investigated and the types and Eskişehir and the parcels in Eskişehir were examined, it
models of the structures to be analyzed were deter- was observed that the parcels of the mansard buildings
mined. Then, for these analysis models, the license de- were mostly disjoint parcels, adjacent parcels and corner
tails of the existing projects have been taken into consid- parcels (Fig. 1).
eration. While determining the sections and dimensions
in the plans, TS-500 (2000), TS-498 (1997) and DBYBHY 2.2. Coding of building models to be analyzed and
(2007) controls were made by using IdeCAD (2014), and mold plans
analyses of the selected sections of mold patterns were
made in SAP2000 (2016). From here, the base shear The coding of the structural models for 120 analysis
forces, shear values and moment values formed under in the study was preferred for the convenience of naming
the mansard layer were obtained. The graphs of these graphics drawings, charts and processes. While coding,
values were drawn and the interpretation of the graphs each account model was given names and it was aimed
were used to investigate the behavior of the mansard to archive the accounts while trying to make it easier to
roof plans at different parcels types, different spans and read and record the data (Kanber, 2018).
storey heights, along with appropriate value conditions. In coding, the first digit is arranged to indicate the
These results were evaluated together with the previous number of storeys, the next digit is span, and the last
analysis results and estimation curves and graphs were digit is Parcel. 3-span models have 3 X-direction spans
created. and 3 Y-direction spans. The distance between each span
These curves and graphs were evaluated together and is 4 meters. Pattern plans are symmetrical in X and Y
real solutions and forecasting graphs were overlapped. terms, thus preventing torsion irregularities. The mini-
Thus, light was shed on the future with the prediction mum sections were determined using IdeCAD (2014)
values of different storey and span solutions. prior to entering data into SAP2000 software. The col-
umns are 40x40 cm, the beams are 25x36 cm and the
slabs are 12 cm. In Fig. 2, mold plans are given for 3
2. Materials and Models spans, 4 spans, 5 spans and 6 spans.
The soil class was determined as Z3 since it is a com-
According to the information obtained from DBYBHY mon ground class in Eskişehir, and it was taken as
(2007), Eskişehir province is a province located geo- Ta=0,15 s, Tb=0,6 s. Z3 elastic acceleration spectrum of
graphically in the Central Anatolia region and in the Por- the local soil class used in the analysis, special design ac-
suk Basin. Eskişehir due to its location in Porsuk basin, celeration spectrum according to DBYBHY (2007) was
generally has a clayey and silty soil. In general, structur- used. Characteristic compressive strength of concrete
ing is concentrated in areas where Z2 and Z3 ground was assumed as 25MPa, Modulus of elasticity is 30000
group are located. Eskişehir is classified as a second-de- MPa. The coefficient of thermal expansion is 0.00001,
gree earthquake region. Poisson's ratio is 0.2. S420 grade reinforcement is se-
Eskişehir's Central Districts are Tepebaşı and Odun- lected as longitudinal and winding reinforcement. The
pazarı districts. In line with the information received characteristic strength of the equipment was taken as
from the provincial municipalities, the number of sto- 420 MPa. Elasticity module has been taken as 200000
reys in the analysis models has been determined as 3, 4, MPa and tensile strength as 500 MPa.

Fig. 1. Representation of disjoint parcels, adjacent parcels and corner parcels.

64 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71

Fig. 2. Schematic representation of the pattern plan for 3 spans , 4 spans, 5 spans and 6 spans.

3. Analysis Results
3.1.2. Base shear force graph created by holding the
3.1. The results of the analysis obtained when the parcel option fixed
parcel is constant, the number of storeys and the
openings are variable, and it's evaluation In this section, the base shear forces are graphically
drawn and evaluated. When drawing graphs, series were
The change between the values was observed by created, these series were created for 3 span, 4 span, 5
keeping the parcel option fixed. Thus, the effects of the span and 6 span.
parcel condition on a reinforced concrete structure were The change in shear force in Fig. 4 was obtained by
investigated. 12 analysis were performed for each 3, 4, 5, fixing the parcel type in the corner parcel. The base shear
6, 7 and 8-storey models. In this way, model analysis forces of the corner Parcel are very close to the adjacent
group with mansard accounts to 72 units. As a result of and disjoint parcel.
the analysis; 3 span corner parcel moments are more
than 66% adjacent and more than disjoint parcels. 4 3.1.3. Moment graph created by keeping the parcel
span corner parcel moments are more than 53% adja- option fixed
cent and more than disjoint parcels. 5 span corner parcel
moments are more than 53% adjacent and more than In this section, parcel option is fixed and series are
disjoint parcels. 3 span corner parcel moments are more created, graphics are defined. While creating these se-
than 36% adjacent and more than disjoint parcels. ries, groups for 3 span, 4 span, 5 span and 6 spans were
formed and these groups were discussed in the same
3.1.1. Vertical forces graph created by keeping the parcel graphs.
option constant In Fig. 5, column moments are given together with the
change of aperture on the corner parcel. This change in-
Graphic movements have been examined as the verti- creases with the increase in openness and the increase
cal force graphs were evaluated and the parcel status re- in the number of storeys.
mained constant. The effect of the openness on the ver- Considering the column moment of Mansard and
tical force was studied by evaluating the vertical forces non mansard structures; With a mansard roof struc-
together with the series. ture, the moments of a 3-storey and 3-span structure
When the Fig. 3 is examined, the vertical forces of the are close together, with the increase in the number of
base shear force the 6 span are increased for the disjoint spans and storey, and the difference between the col-
parcels. The graphics for the mansard and the non struc- umn moments of Mansard and non mansard structures
ture are provided together. increases. It is observed that the main factor in this dif-
It was observed that the proportional increases in Fig. ference is not increase in the storeys but increase in the
3 were also very close to the adjacent and disjoint parcels. openness.
 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71 65

110110
Fz Vertical Force(KN) ------mansard ------- non mansard

97780
120000

85455
77500

73120
100000

68810

60790
60121
51430

98650
50590
80000

48460
44910

42730
39229

86320
34049
33540
29400
60000

27860

73990
26090
22781

69520
22175
19460
4K-3a-K 16570 16150

61660
60830
3K-3a-K13250 12838
40000

52140

49320
45470

43450
26070
39790

37000
20000

34100

34760
26510
6K-3a-K 23190

5K-4a-K 28420
5K-3a-K 19880

4K-4a-K 22730
9940

3K-4a-K17050
0
7k-3a-K
8k-3a-K

7k-4a-K
8k-4a-K

7k-5a-K
8k-5a-K

7k-6a-K
8k-6a-K
6K-4a-K

3K-5a-K
4K-5a-K
5K-5a-K
6K-5a-K

3K-6a-K
4K-6a-K
5K-6a-K
6K-6a-K
Fig. 3. Vertical forces of columns for the corner parcel when the parcel option is fixed.

Base Shear Force F (KN) ------mansard ------- non mansard

1620
1800

1430
1600

1272
1140
1400

1070
1010

1450
1200

898

880

1270
750

750
1000

720
660

620

1080
589

800

1020
508
490
440

900
410

890
390
345

600
333
290

760
240

720
194

670

640

400
590

510

530
500

370

200
420
390
340

330
240

290
200

250

0
150

7k-3a-K
8k-3a-K

7k-4a-K
8k-4a-K

7k-5a-K
8k-5a-K

7k-6a-K
8k-6a-K
3K-3a-K
4K-3a-K
5K-3a-K
6K-3a-K

3K-4a-K
4K-4a-K
5K-4a-K
6K-4a-K

3K-5a-K
4K-5a-K
5K-5a-K
6K-5a-K

3K-6a-K
4K-6a-K
5K-6a-K
6K-6a-K
Fig. 4. Base shear forces of F columns for the corner parcel when the parcel option is fixed.

Column Moments (KN.M) ------mansard ------- non mansard

25796

30000
22572
19348
19150

25000
16756

15800
14363
14231

20000
13140
12453

21319
11110
10672
10601

18655

15000
9273

9230
7950

7250

15990
15827
6020

5663
13848

10000
13320
7500 4320
4210
3490

11870
11761
2723
2589

10650
10292

9380
8820
8761

5000
7664
6570

5K-4a-K 6140
3580

4K-4a-K 4910
2860

3570

4680
2140

0
3K-4a-K2250
7k-3a-K
8k-3a-K

7k-4a-K
8k-4a-K

7k-5a-K
8k-5a-K

7k-6a-K
8k-6a-K
3K-3a-K
4K-3a-K
5K-3a-K
6K-3a-K

6K-4a-K

3K-5a-K
4K-5a-K
5K-5a-K
6K-5a-K

3K-6a-K
4K-6a-K
5K-6a-K
6K-6a-K

Fig. 5. Graph of column moments for corner parcel when parcel option is held constant.

3.2. Analysis results and evaluations when the 3.2.1. Vertical forces formed by keeping the number of
numbers of storeys, fixed parcels and openness are storeys constant
variable
Vertical force graphs are listed below when the storey
When the number of parcels and the number of spans quantity is kept constant. For the vertical forces, the
(3, 4, 5, 6, 7 and 8 storeys) of the building with mansard forces of the mansard and non mansard structures are
roof are variable, the values obtained as the result of the given together. Force differences between mansard and
analysis are obtained as base shear forces, column mo- non mansard structures are increasing with increasing
ments and top displacement. openness.
66 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71

When keeping the storey quantity constant for 5 sto- and non mansard buildings is also increasing in case of
reys, the graphs were drawn so that the values of the ad- increase in openness for 6 storeys. The same propor-
jacent and corner parcel were examined. tional increases were found for 3 storeys, 4 storeys, 6
As shown in Fig. 6, in a 5-storey structure, the number storeys, 7 storeys and 8 storeys.
of storeys and the fixed opening value were determined
as variables in the same graph. Looking at these varia- 3.2.3. Graph of moment forces generated by keeping the
bles, 3 span, 4 span, 5 span and 6 spans appear together. number of storeys constant
The proportional increases observed in Fig. 6 were
also found for 3 storeys, 4 storeys, 5 storeys, 7 storeys In this section, the storey number is fixed and the se-
and 8 storeys. ries is formed for 3 span, 4 span, 5 span and 6 spans on
These graphs which are formed by keeping the storey the chart. These series are evaluated together. Thus, the
quantity constant shows us that the effect of parcel type effect of the parcel type on the structure is intended for
change on vertical forces is low. In addition, it is under- evaluation.
stood that the situation does not change with the increase In Fig. 8, the number of storeys for 5 storeys was fixed
in the number of storeys and although the number of sto- and the graphics of the structures with and without Man-
reys changes, this increase is similar to each storey. sard were drawn together. Although the structure with
mansard and the structure without Mansard increase in
3.2.2. Shear force graph created by keeping the number openness, the change of the parcel did not affect the mo-
of storeys constant ment values.
When we look at the moment graphs created by keep-
In Fig. 7, the shear force is not affected by the change ing the storey quantity constant, it is determined that the
in the parcels, although the shear force increases with moment values for the same storey are independent of
the increase in the openness. the parcel condition. When the moment values are eval-
In Fig. 7, the shear force of mansard and non mansard uated together for mansard and non mansard structures,
structures are parallel to the horizontal axis and this the difference in the two structure values is increasing in
shows that the shear force is not affected by the parcel the column moments formed at the base with the in-
condition. The difference in shear force between mansard crease in the openness in these graphs.

------mansard ------- non mansard

73120
73110
Fz Vertical Force(KN) 72410
80000
70000
51430
51410
50830

60000
61660

61660

61660
50000
33540
33530
33070

40000
43450

43450

43450
19450

19460
19110

30000
20000
28420

28420

28420

10000
16570

16570

16570

0
5K-3a-A

5K-3a-B

5K-3a-K

5K-4a-A

5K-4a-B

5K-4a-K

5K-5a-A

5K-5a-B

5K-5a-K

5K-6a-A

5K-6a-B

5K-6a-K

Fig. 6. Vertical force graph created by keeping the storey quantity constant for 5 storeys.

Base Shear Force F (KN) ------mansard ------- non mansard

1070

1070

1070

1200
1000
750

750

750

800
900

900

900
505

490

490

600
640

640

640
290

290

290

400
420

420

420

200
240

240

240

0
5K-3a-B

5K-3a-K

5K-4a-K

5K-5a-B

5K-5a-K

5K-6a-K
5K-3a-A

5K-4a-A

5K-4a-B

5K-5a-A

5K-6a-A

5K-6a-B

Fig. 7. Base shear force graph created by keeping the storey quantity fixed for 5 storeys.
 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71 67

Column Moments (KN.M) ------mansard ------- non mansard

15800

15800
15650
18000
16000

11110

11110
10980
14000
12000

13320

13320

13320
7250

7250
7150
10000
8000

4210

4210
4130

9380

9380

9380
6000
4000

6140
6140

6140
3580

3580
2000
3580

0
5K-3a-A

5K-3a-B

5K-4a-A

5K-4a-K

5K-6a-K
5K-3a-K

5K-4a-B

5K-5a-A

5K-5a-B

5K-6a-A
5K-5a-K

5K-6a-B
Fig. 8. Moment graph created by keeping the storey quantity constant for 5 storeys.

3.3. Analysis results and evaluation when the 8th storey. While the shear force increases linearly from
openness is constant, the number of storeys and the 3rd storey to 6th storey, the curvature angle of this linear
parcel option is variable graph is very little affected by the change in the parcel
change.
It is aimed to see effect values by keeping openness
constant. The parcel option and the number of layers 3.3.2. Graph of shear forces when the span is held constant
were variable when the spans was kept constant. When
the number of spans with mansard roof is fixed, parcel Fig. 10 shows a linear increase of the base shear forces
and storey quantity is variable, the values of the base given for 5 spans. The increment slopes of the disjoint
shear forces, column moments and top displacement ob- parcel, adjacent parcel and corner parcels are the same.
tained as a result of analysis are examined. Graphs are Mansard and non mansard buildings are provided to-
drawn for base shear force, column moments and top gether. The slope in the shear graph of Mansard and non
displacement values. mansard is the same. The same proportional results
were found in 3 spans, 4 spans and 6 spans.
3.3.1. Vertical forces graph when the aperture is held
constant 3.3.3. Moment graph when opening is fixed

The effect of vertical forces was observed by keeping In Fig. 11, moment values were taken by keeping the
the aperture constant. The increase in the number of sto- openness constant, and it was observed that the parcel
reys increases the vertical forces. The parcel variable variable was not affected when evaluating the 5 open-
does not affect the vertical forces very much when look- ness in different parcels. The same proportional results
ing at the adjacent parcel and the corner parcel from the were found for 3 spans, 4 spans and 6 spans.
disjoint parcel. When the span is held constant moment graph shows
In Fig. 9, the vertical forces given for 5 openings show increase from the 3rd storey to the 8th storey. When
a linear increase. The increment slopes of the disjoint looked at the parcel change, disjoint, adjacent and corner
parcel, adjacent parcel and corner parcels are the same. parcels show a very close moment change ratio. The dif-
The same proportional results were found in 3 spans, 4 ference between the moment values of mansard and non
spans and 6 spans. When the angle is fixed, it is observed mansard structures are increasing as we move from 3
that the motion of the shear force is linear from 3rd to spans to 6 spans.

Vertical Force Fz (KN) ------mansard ------- non mansard

77490

77500
76900

90000
68810
68790
68210

80000
60109

60121
59528

51430
51410
50830

70000
42720

42730
42140

60000
69520

69520

69520
34038

34049
33456

50000
60830

60830

60830
52140
52140

52140

40000
43450

43450

43450

30000
34760

34760

34760

20000
26070

26070

26070

10000
0
8k-5a-A

7k-5a-B
8k-5a-B

7k-5a-K
8k-5a-K
7k-5a-A
5K-5a-A
3K-5a-A
4K-5a-A

6K-5a-A

3K-5a-B
4K-5a-B
5K-5a-B
6K-5a-B

3K-5a-K
4K-5a-K
5K-5a-K
6K-5a-K

Fig. 9. Vertical force graph created by keeping the openness constant for 5 spans.
68 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71

Base Shear Force(KN) ------mansard ------- non mansard

1140

1140

1140
1010
1010

1010
1200

898

898
890
1000

750

750

750
1020

1020

1020
800

620

620

620
890
890

890
508
508
500

760

760

760
600

640

640

640
400 510

510

510
370
370

370
200

0
7k-5a-A
8k-5a-A

7k-5a-B
8k-5a-B

7k-5a-K
8k-5a-K
3K-5a-A

6K-5a-A

3K-5a-K
4K-5a-K
5K-5a-K
6K-5a-K
4K-5a-A
5K-5a-A

3K-5a-B
4K-5a-B
5K-5a-B
6K-5a-B
Fig. 10. The base shear force graph created by keeping the span constant for 5 spans.

Column Moments(KN.M)
25000
19150

19150

19150
16756
16756

16756
20000
14363

14363

14363
11110

11110
10980

15000
15827

15827

15827
9230

9230
9110

13848
13848

13848
10000
11870

11870

11870
4320
4320

4320
9380

9380

5000 9380
7500

7500

7500
3570

3570

3570

0
7k-5a-A
8k-5a-A

7k-5a-B
8k-5a-B

7k-5a-K
8k-5a-K
3K-5a-A

6K-5a-A
4K-5a-A
5K-5a-A

3K-5a-B
4K-5a-B
5K-5a-B
6K-5a-B

3K-5a-K
4K-5a-K
5K-5a-K
6K-5a-K

Fig. 11. Moment graph generated by keeping the span constant for 5 spans.

3.4. Creating forecasting functions graph of reinforced concrete mansard roof and non man-
sard roof is given, and in Fig. 13, the graph of mansard
Based on the results obtained from these analyses, roofed structure group is given. In Fig. 12, parabolic
graphs were drawn for each set of results, and most ap- graph inside the F force is examined for the non mansard
propriate mathematical functions were obtained from reinforced concrete structure. Figs. 12 and 13 show a
these graphs. How close these functions are to reality is parabolic graph and it is understood that equations can
also verified by comparing the solutions of intermediate be obtained from these graphs.
values (such as storey counts. etc.). Thus, a forecast pro- As shown in Fig. 14, the given values are defined as
jection of the base cut and moment values has been cre- parabolic equation by matching with some values in the
ated depending on the openings and parcel variables series. The values in this graph are determined by the ac-
from 3rd storey to 10th storey. tual results obtained from the analysis. Fig. 13 shows us
Firstly, the parcel variable is fixed and the graphics that these graphs can be connected to specific formulas
are defined. Parabolic graphs are placed on the graphs in the series formation. It is understood that new graphs
formed according to these definitions. The reason for the can give prediction values for new series.
formation of parabolic charts and the formation of In Fig. 15, the data obtained by using the analysis pro-
graphs is the form of increasing graphics curves. gram of the 10-storey building was found to be in the
A new graphic definition has been created by combining mobile wave area.
the solution series and is tried to understand the relation If this series is expanded and replicated by this qual-
between this graphic definition and the solution series. ity, it will multiply in the same quality as the parabolic
In Fig. 12, a parabolic chart was used for trying to cap- cone. Due to this proliferation, it will be expected that the
ture the motion of the variables in the following units, and values in different storey and span structures will re-
these values were moved on the X axis within them. main between these ranges. When the integral of these
These values are shifted in line with the X axis, giving a functions is taken, value interval estimation can be made
parabolic graph and shown in Fig. 13. In Fig. 12, parabolic within the new series that will be formed.
 FX Base Shear Force (KN)

0
50
100
150
200
250
300
350
400
450
500

1000
1200
1400

200
400
800

600

0
200
400
600
800
1000
1200
1400
1600
1800

0
3K-3a-A 150 190
3K-3a-A
3K-3a-K

194
4K-3a-A 200 240
4K-3a-A

Base Shear Force (KN)

5K-3a-A 240 290 5K-3a-A
4K-3a-K

240
6K-3a-A 290 341 6K-3a-A
7k-3a-A 340 390 7k-3a-A
440
3K-4a-K 8k-3a-A

333
8k-3a-A 390
3K-4a-A
4K-4a-A
4K-4a-K

410
3K-3a-B 150 194 5K-4a-A
4K-3a-B 200 240 6K-4a-A
3K-5a-K 7k-4a-A

508
5K-3a-B 240 290
8k-4a-A
6K-3a-B 290 345
3K-5a-A
4K-5a-K

620
7k-3a-B 340 390
4K-5a-A
440
8k-3a-B 390 5K-5a-A
5K-5a-K

750
6K-5a-A
3K-3a-K 150 194 7k-5a-A
Fig. 12. Parabola placement on drawn graphics.

Fig. 14. Defining a parabolic rectifier for force F.

8k-5a-A
y = 1,5834x2 + 4,8806x + 220,3 NON MANSARD

6K-5a-K

898
4K-3a-K 200 240

Fig. 13. Analysis of base shear force graph as series.

3K-6a-A
240 290
Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71

5K-3a-K 4K-6a-A
5K-6a-K 6K-3a-K 290 345

1070
5K-6a-A
y = 1,5311x2 + 12,212x + 249,51 MANSARD

7k-3a-K 340 390 6K-6a-A

6K-6a-K 8k-3a-K 390
7k-6a-A

1272
440 8k-6a-A
69
70 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71

3000

2500
BASE SHEAR FORCE (KN)

2000 y = 42,5x2 + 180,5x + 217,5

1500

1000

500
y = 15x2 + 51x + 85

10K-5a
4K-3a

10K-3a

7K-4a

10K-4a

10K-6a
3K-3a

5K-3a
6K-3a
7K-3a
8K-3a
9K-3a

3K-4a
4K-4a
5K-4a
6K-4a

8K-4a
9K-4a

3K-5a
4K-5a
5K-5a
6K-5a
7K-5a
8K-5a
9K-5a

3K-6a
4K-6a
5K-6a
6K-6a
7K-6a
8K-6a
9K-6a
Fig. 15. 32 Piece 3rd to 10th storey estimated series graphical drawing.

The determination of these prediction functions for prediction curve. The equation graph was drawn in line
the shear force is also done for the moments and the val- with the results obtained from the average displacement
ues of the analysis are processed in the series on the values and a 20-storey structure of series was added to
chart. The moment values of the 10-storey reinforced the sub-axis on this equation. Thus, a prediction curve
concrete structure remain within this graph range as has been formed for the displacement values of the struc-
shown in Fig. 16. Therefore, in this series consisting of 3 tures up to 20 storeys. It was observed that this value was
storeys to 10 storeys, 3 spans to 6 spans and the parcel very close when structural analysis for 20 storey build-
can be estimated value range depending on the situation. ings was added to the prediction curve. The graphs cre-
A curve was drawn to the average displacement val- ated together with the set of values from here shed light
ues and the displacement values of the 20-storey struc- on the prediction of new values. Thus, it has been re-
ture were added on this curve. In this way, it is seen how vealed that the other displacement values remaining
close the real values of the 20-story structure are to the within the range can be estimated using Fig. 17 chart.

40000

35000 y = 20.944x2 + 213.5x + 8587

COLUMN MOMENTS (KN.M)

30000

25000

20000

15000

10000

5000
y = 6.3194x2 + 5.6833x + 1957.5
0
10K-4a
10K-3a

10K-5a

10K-6a
8K-4a
9K-4a

3K-5a
4K-5a
3K-3a
4K-3a
5K-3a
6K-3a
7K-3a
8K-3a
9K-3a

3K-4a
4K-4a
5K-4a
6K-4a
7K-4a

5K-5a
6K-5a
7K-5a
8K-5a
9K-5a

3K-6a
4K-6a
5K-6a
6K-6a
7K-6a
8K-6a
9K-6a

Maksimum Moment Minumum Moment

Fig. 16. 32 Piece graphical drawing from 3rd storey to 10th storey.
 Şengel et al. / Challenge Journal of Structural Mechanics 5 (2) (2019) 62–71 71

25

y = 0.0435x2 + 0.1738x + 0.2662

20
AVERAGE DİSPLACEMENT (CM)

AVERAGE Y = 0,0435X2 + 0,1738X + 0,2662

15

10

0
10 KATLI

11 KATLI

12 KATLI

13 KATLI

14 KATLI

15 KATLI

16 KATLI

17 KATLI

18 KATLI

19 KATLI

20 KATLI
3 KATLI

4 KATLI

5 KATLI

6 KATLI

7 KATLI

8 KATLI

9 KATLI

Fig. 17. Average displacement graph.

4. Conclusions Analysis results can be defined by graphs and func-

tions with the minimum and maximum values of the base
In this study, 96 mansard and 24 non mansard model shear forces and moments listed by series. Thus, the es-
analyzes were performed for the reinforced concrete timation range for different storeys and openings was
structure. Values from these structures up to 3 to 8 sto- defined and the estimation projection was determined
reys and from 3 openings to 6 openings were defined by the expansion of the series in the solutions of the de-
and analyzed in the light of Eskişehir license information fined equations.
and their results were evaluated. As a result of these eval- Equations are formed by the results obtained from
uations, the increase in storey and openness increases the the average displacement values. Since displacement is
increase in parabolic base shear and column moment in- not affected by openness, an estimate of the values to be
creases on the structure. As a result of the investigations, formed on different storeys was carried out with a single
it was observed that the displacement values were very prediction equation.
close to each other when the effects of displacement val- In this study, symmetric models are used, it is recom-
ues on the same storey buildings were examined. This mended to analyze non-symmetric systems in future
shows that the value of displacement is too small to be studies and so an approach for all symmetric and non-
taken into account. In this study, it is understood that symmetric systems can be developed. In addition, this
displacement values are independent of openness. study can be done by increasing the number of solutions
As a result of the analyses obtained from models with and analyzes in the set of values and increasing the sen-
different spans and storeys, base shear force, column sitivity for estimation graphs.
moments and top displacement values were evaluated in
charts and graphs. It is estimated that the function we
obtain depends on the set of values of these series can be REFERENCES
obtained by the user, depending on the prediction pro-
jection, without making any analyses based on the differ-
ent number of layers. Functions have been created and DBYBHY (2007). Regulation on Buildings to be held in Earthquake Ar-
equations have been written in defined series. These eas. General Directorate of Disaster Affairs, Earthquake Research
functions are created for base shear force, column mo- Department, Istanbul, Turkey.
IdeCAD (2014). Concrete Analysis Program. Version ideCAD 7,022,
ments and top displacement values. New series are de- 6500HL-3109 Static.
fined and graphs are drawn in accordance with these Kanber İ (2018). Analysis of Reinforced Concrete Mansards Roof Struc-
new series. 10-story and 20-story buildings, 3 spans to 6 tures Dependent on Different Plan Types. M.Sc. thesis, Eskişehir Os-
spans were analyzed and the new series were added as mangazi University, Eskişehir, Turkey.
a point value to the graphs of the defined series. Based SAP2000 (2016). Finite Element Analysis Program. Version SAP2000 v
on the results of the analysis, it was determined that the 17.2.0.
TS–498 (1997). Calculation of Loads to be taken for Sizing of Building
function graphs created for estimation remained within
Elements Values. Turkish Standards Institute, Ankara, Turkey.
the range. The graphics and the functions that will be ob- TS–500 (2000). Design and Construction Rules of Reinforced Concrete
tained from the range that is defined as series are able to Structures. Turkish Standards Institute, Ankara, Turkey.
create a prediction interval about the base shear force, Üstün B, Kolsal F (2016). Mansard roof in Eskisehir urban architecture
colon moments and peak displacement values of the effects. 8. National Roofing & Facade Symposium. Mimar Sinan Fine
models that will sustain the mentioned series, which Arts University, Istanbul, Turkey, 1-7.
have different openness' and storey counts.