Time history analysis of braced and unbraced steel Structure. Icerie 2017 paper_1

1. ICERIE_ MIE_XYZ
* Corresponding author: shovonakhusru@yahoo.com
Proceedings of the
International Conference on Engineering Research, Innovation and Education
2017
ICERIE 2017, 13 ̶ 15 January, SUST, Sylhet, Bangladesh
Time History Analysis of Braced and Unbraced Steel Structures
S. Khusru1*, M. M. Rahman2 ,M. K. Alam3 , F. Mujib3 & S. Das3
1
Assistant Professor, Department of Civil Engineering, Ahsanullah University of Science and
Technology, Dhaka 1208.Email: shovonakhusru@yahoo.com
2
Professor, Department of Civil Engineering, Ahsanullah University of Science and Technology,
Dhaka 1208. Email: mahmud402@yahoo.com
3
Graduate Student, Department of Civil Engineering, Ahsanullah University of Science and
Technology, Dhaka 1208.
Email:khorshed395@yahoo.com,pritha222@yahoo.com,soumitra.dr@gmail.com
Keywords:
 Time history
analysis
 Steel structures
 Concentric
bracing
 Eccentric
bracing
Abstract: This paper investigates and compares the behavior of steel braced
structures with the help of time history analysis with the purpose of designing the
most effective steel structure for resisting the lateral loads caused by earthquakes.
In this study, a ten-storied building comprising of 2800 sqft plan area was first
designed with sophisticated finite element software called SAP 2000 V14 by
incorporating gravity load as per BNBC. The building was optimally redesigned
with concentric and eccentric bracing system. Earthquake data of Imperial Valley
for four different magnitudes such as 5.0, 5.5, 5.6 and 6.95 have been selected for
time history analysis. The parameters for the study were column bending
moment, shear force and joint displacement. It is concluded from observing the
results of dynamic analysis that the cross braced structure carries higher bending
moment and shear force at base of corner column than the other two cases. The
cross braced structure gives small displacement than unbraced type of structure
which is 0.21 inch. Concentrically braced structure is 1.05 times and unbraced
structure is 1.15 times of the weight of the eccentrically braced structure. So the
study concludes that eccentric braced is more economic than cross braced system
but the cross braced system is considered safer due to the displacement, moment
and shear being more than that of eccentric braced structure.
1. INTRODUCTION
One of the important issues to consider for the design of steel structures is reducing the damage cause by
earthquakes. For this time history analysis of braced and unbraced steel structures is an effective solution for
designing the most economic and safe structure which can reduce the damage to a desirable outcome. Steel
braced frame is one of the structural systems used to resist lateral loads in multistoried buildings. Concentrically
braced frames increase the lateral stiffness of the frame and usually decrease the lateral drift. However, increase
in the stiffness may attract a larger inertia force due to earthquake. Eccentrically bracings reduce the lateral
stiffness of the system and improve the energy dissipation capacity. The catastrophic damage caused by recent
major earthquakes has greatly increased public awareness of the seismic risks in building construction. Since the
1994 Northridge earthquake in California, there have been new concerns about the safety and performance of
steel moment resisting frame (SMRF) structures because of the extensive damage later found in many modern
steel buildings as a result of that earthquake (Tremblay et al., 1996). A thesis performed on Inelastic Behavior of
Eccentric Braces in Steel Structure (Nourbakhsh S., 2011) shows that using the eccentric diagonal braces for
low and medium rise structures is more logical and acceptable from economical point of view as this type of
bracing system absorbs considerably more energy when compared with eccentric V and Inverted V bracing
systems.
A full time history analysis will give the response of a structure over time during the application of dynamic
loading. With the advancement of seismic design of structures time history analysis has become an effective

2. parameter. Bangladesh being vulnerable to earthquake dynamic analysis is a must for the future design of steel
structures in major earthquake zones considering the best economic bracing patterns.
The two important parameters that can influence the type of the structural system which are supposed to be
used, especially the type of the bracing systems in a structure, economy and performance parameters. This paper
is developed to produce the civil engineers a scenario on the effectiveness of bracing system under lateral
loading. Alongside this study will also provide a guideline for the effective selection of bracing. Joint
displacement under different bracing condition for same loading condition will also be provided in an
understandable way.
2. METHODOLOGY
For analytical application a simple ten storied plan of 2800 square feet floor area has been chosen to apply
time history loading. The building was optimally designed following Bangladesh National Building Code
(BNBC 2006) under gravity loading and then design was repeated and eccentric bracing and cross bracing were
used. Fig. 1 below shows the layout plan of the building.
Fig.1 Layout Plan of the Building.
There are three frames consisting of columns and beams running along the building longitudinally.
Transverse beams connect the four longitudinal frames. A three dimensional view of the steel building
without bracing, eccentrically braced and concentrically braced is shown in figure 2. All external frames are
braced by bracing systems placed only at corner panelsin both directions. Beams and columns have been
designed with W steel sections and each bracing system has been analyzed angle L8x8x9/8 for eccentrically
braced and double angle 2Lx 3.5x 5/16 section for cross braced structures.
Fig.2 Three dimensional view of (a) unbraced, (b) eccentrically braced and (c) cross braced structure.
(a)Unbraced (b)Eccentrically braced (c) Cross braced

3. 3 | S. khusru et. al., I C E R I E 2 0 1 7
All building models are considered as Ordinary Moment Resisting Frame with Steel beam and column and
6 inch concrete slab. Except grade beams and beams in top floor identical beam sections have been maintained
for similar elevation for symmetric design. In this study, fixed base restraint is used which restrain all six degree
of freedom. Ten different diaphragms have been assigned for ten different storeys. For simplification of study
same sections has been used for all bracing systems. For all steel members, A992Fy50 steel has been used.
AISC-ASD method has been followed for member design. For the time history analysis of the said structures
SAP 2000 V14 had been used. The steel building is analyzed with considering different load combinations as
per BNBC.
Table 1 Applied loading on the structures.
Type of load Name of load Value Unit
Super Dead Floor finish 25 psf
Partition wall 25 psf
Lime concrete on roof 30 psf
Live load Live 60 psf
Earthquake
Loading
Imperial Valley-1940 of Magnitude 6.95
Imperial Valley-1938 of Magnitude 5
Imperial Valley-1951 of Magnitude 5.6
Imperial Valley 1953 of Magnitude 5.5
All type of dead loads, which will be subjected to the structures, is defined in model using BNBC code. The
applied loads on the structure are given in the table 1. Linear modal time history analysis has been used in this
study with damping ratio 5%. The earthquake loadings were downloaded from the Peer database (Website-
http://peer.berkeley.edu). In case of selecting earthquake data for using as input in time history analysis,
different magnitude of earthquake was taken into consideration.
3. RESULT AND DISCUSSION
The lateral deflection along with moment and shear for columns that take place in all the structural system
had been determined and also their design output, considering provided weight, to evaluate the most economical
structural system with improved stiffness in frame has been compared. Those parameters are column bending
moment, column shear force, and joint displacement and serviceability criteria of Structure. The parameters for
this analysis are-
 Column bending moment for exterior and interior column
 Shear force for exterior and interior column
 Joint displacement for exterior and interior column
3.1 Column Bending Moment for Dynamic Analysis
In order to study column bending moment, two columns have been selected. One is exterior corner column
C1 and other is interior column C4 as shown in layout plan in fig.1.
(a) Unbraced (b) Eccentric braced

4. (c) Cross braced
Fig.3 Column Bending Moment for (a) Unbraced, (b) Eccentric braced and (c) Cross braced Structure for
exterior corner column.
From fig. 3 it can be seen that maximum moment for exterior corner column is found for the earthquake
Imperial Valley 1940 of magnitude 6.95. Comparing the three graphs of fig.3 it is seen that maximum value is
1050 kip-ft for cross braced structure whereas unbraced structure showed moment 490 k-ft which is almost 50%
of the maximum moment due to the same loading. Although for other three earthquakes magnitude varies as 5,
5.5 and 5.6 but all three cases shows almost similar results. For all the structures the maximum value is observed
at the base and decreases gradually towards the top of the structure.
(a) Unbraced (b) Eccentric braced
(c) Cross braced
Fig.4 Column Bending Moment for (a) Unbraced, (b) Eccentric braced and (c) Cross braced Structure for
interior column.

5. 5 | S. khusru et. al., I C E R I E 2 0 1 7
However, in case of interior column C4, the result is different as shown in fig. 4. Maximum bending moment
has been observed in case of unbraced structure i.e. 620 k-ft for Imperial Valley 1940 of magnitude 6.95 and
minimum value 109.8 k-ft is for eccentric structure.
3.2 Shear Force for Dynamic Analysis
Shear force has been evaluated for both interior column C4 and exterior column C1 for all the three
structures for different earthquake loadings. The behavioral pattern of shear force diagrams are not same as it
can be seen in the following figures.
In fig. 5, the results shows that for all cases, the structure with cross brace carries higher shear force with
the value 207 kip at base level of C1 than the other two cases for different earthquakes. Also the eccentric
braced type is higher than unbraced type which has the lowest values. The minimum shear force for exterior
column is at the base of the unbraced structure which is 49 kip. Cross braced structure carries 4.2 times shear
than unbraced structure for exterior corner column.
(a) Unbraced (b) Eccentric braced
(c) Cross braced
Fig.5 Shear force diagram of (a) Unbraced, (b) Eccentric braced and (c) Cross braced
Structure at different storey levels for exterior corner column.
In case of interior column C4, shear force diagram pattern varies with a drop in shear value in storey 3 for the
braced structures. Although maximum value has been found for Imperial Valley 1940 of magnitude 6.95.
Unbraced structure has the maximum shear for interior column with the value 80 kip as shown in fig.6 and
minimum value for the same earthquake loading is observed at the eccentric braced structure with a highest
shear of 13 kip, which is maximum for this structure.

6. The minimum shear is found for Imperial Valley 1953 of magnitude 5.5 near to 1 kip. Unbraced structure
carries 6.2 times shear for central column than eccentrically braced structure.
(a) Unbraced (b) Eccentric braced
(c) Cross braced
Fig.6 Shear force diagram of (a) Unbraced, (b) Eccentric braced and (c) Cross braced Structure at
different storey level for interior column.
3.3 Joint Displacement
In case of joint displacement, the Imperial Valley 1940 of magnitude 6.95 showed maximum displacement
in all the structures. The displacement values increased gradually from base and showed maximum values at top
in all the structures.
Fig. 7 showed the joint displacement at different storey levels of exterior corner column C1. The unbraced
structure showed the maximum displacement value of 0.48 inch at top whereas the maximum displacement for
eccentric braced is 0.2 inch at top and for cross braced it is less than 0.0005 inch.
For interior column the similar pattern is observed as showed in fig.8 with the maximum value for unbraced
structure and minimum value for cross braced structure. For interior column maximum displacement at roof is
for unbraced and eccentric braced structure with the value 0.5 inch and minimum for cross braced structure with
the value 0.2 inch at top.

7. 7 | S. khusru et. al., I C E R I E 2 0 1 7
(a) Unbraced (b) Eccentric braced
(c) Cross braced
Fig.7 Variation of joint displacement for (a) Unbraced, (b) Eccentric braced and (c) Cross braced Structure at
different storey levels for exterior corner column.
It may be said that the unbraced type of structure gives higher displacement than the other two cases for
different earthquakes. Also the cross braced structure gives smaller displacements than unbraced type of
structure.
(a) Unbraced (b) Eccentric braced

8. (c) Cross braced
Fig.8 Variation of joint displacement for (a) Unbraced, (b) Eccentric braced and (c) Cross
braced Structure at different storey levels for interior column.
4. SERVICEABILITY CRITERIA
In order to determine the performance of these structures under dynamic loading the weight of these
structures has been calculated. The fig. 9 (a) shows the unit weight of three types of structural system in kip per
square feet. The figure indicates that the unbraced system has the maximum unit weight (0.063 kip/sqft)
compared to the other two. Again the unit weight of cross braced system (0.058 kip/sqft) is higher than that of
eccentric braced system (0.055 kip/sqft) which is the lowest of all them. The unit weight of eccentric braced is
0.055 kip/sqft which is 1.05 times of concentric and 1.15 times of the unbraced structure.
(a) (b)
Fig. 9 (a) Unit weight versus the types of structural system chart (b) Unit weight x Displacement versus the
types of structural system
Now, multiplying these values with their corresponding maximum displacement it can be said that the higher the
multiplied value the more vulnerable the structure will be in serviceability criteria. Here, it is observed that the
cross braced is more economical and safe than other two types of structure. Eccentric braced system has higher
displacement due to carrying low weight and is considered less safe. But unbraced structure is considered most
uneconomical and unsafe structural system than eccentric and cross braced system. Fig. 9(b) showed the result
it indicates cross braced has the lowest value 0.0116 as compared to unbrace 0.03075 and eccentric braced
0.02783. So it can be said that the cross braced structure can perform better under dynamic loading that
eccentric braced and unbraced structure.
5 CONCLUSIONS

9. 9 | S. khusru et. al., I C E R I E 2 0 1 7
Each parameter in moment, shear and displacement cases shows that the Imperial Valley-1940-6.95 has the
maximum values and the Imperial Valley-1953-5.5 has the minimum values. The summery is given below. The
cross braced type structure carries higher moment 1050 kip-ft at base level of exterior column than the other two
cases for different earthquake cases. Also the eccentric braced type is higher than unbraced type which has the
lowest values. For exterior column the maximum moment is found for the unbraced structure with the value 620
k-ft. Cross braced structure carries 4.2 times shear than unbraced structure for exterior corner column. Unbraced
structure carries 6.2 times shear for central column than eccentrically braced structure.
Unbraced type of structure gives higher displacement than the other two cases for different earthquake
cases. Also the cross braced structure gives small displacement than unbraced type of structure. The result of the
economic comparison of the three types of structure showed that the unit weight of eccentric braced is minimum
with the value 0.055 kip/sqft. Concentrically braced structure is 1.05 times and unbraced structure is 1.15 times
of the weight of the eccentrically braced structure. Even if eccentric braced system seems more economic than
cross braced system but considering product of unit weight and displacement of the three types of structures for
static and dynamic analysis, it is seen that the cross braced system is more economic and safer than the eccentric
braced structure.
REFERENCES
BNBC (2006). Bangladesh National Building code, Housing and Building Research Institute, Dhaka,
Bangladesh, 2nd Edition, pp. 10655, 10608, 10621.
Nourbakhsh, S.M., (2011). Inelastic Behavior of Eccentric Braces in Steel Structure, Master Thesis in Civil
Engineering, Eastern Mediterranean University, Cyprus.
Tremblay, R. et.al. (1995). “Performance of steel structures during 17 January, 1994 Northridge
earthquake.” Canadian Journal of Civil Engineering, 1995, Volume 22 Issue2, pp. 338-360.
http://peer.berkeley.edu dated 13 February 2016
SAP2000. Integrated Software for Structural Analysis and Design: Computers and Structure Inc.,
California.