1.
Alhosn University, Abu Dhabi, UAE
Department of Civil Engineering
Design Assessment of a Reinforced Concrete
Building Through Non-Linear Analysis
Presented by: Mohammed Mohideen Ismail
Ahmad Mahmoud Khier
Moaid Ahmed Jumaa
Adnan Talal Mayassi
Supervised by: Dr George Markou, Assistant Professor
1
2.
1. Project Objectives
2. Methodology
3. Modeling
4. Nonlinear Analysis (Theory)
5. Geometry of the Structure
6. Results from the Preliminary Analysis (Linear Static)
7. Modal Analysis
8. Computation of the Seismic Load
9. Nonlinearities and SAP2000
10. Numerical Results (Nonlinear Analysis)
11. Redesign of the RC Structure
12. Conclusions
Presentation Contents
Wednesday, 29th
of May 2013
2
3.
Study the mechanical behavior of the RC structure.
Perform Pushover Analysis.
Redesign the building so as to achieve a seismically resistant
behavior (if required).
Primary Objectives
Wednesday, 29th
of May 2013
3
4.
Study the geometry of the structure.
Two finite element models were constructed in Etabs and Sap2000 commercial
software through which the seismic assessment of the RC structure was performed.
Determining whether the structure is capable of carrying a medium seismic
excitation according to Eurocode, through the use of pushover analysis.
Perform the redesign.
Methodology
Wednesday, 29th
of May 2013
4
5.
Modeling
Finite Element Method (FEM):
Is a numerical analysis technique used by engineers, to obtain
solution to partial differential equations that describe a wide
variety of physical and nonphysical problems.
Wednesday, 29th
of May 2013
5
6.
Modeling
Types of Finite Elements:
The shape of each element gives the ability to discretize different
geometries according to the structural element shape.
In our model we used beam-column and shell finite elements.
Rod and beam elements
Plane and shell elements
Solid elements
Wednesday, 29th
of May 2013
6
7.
Non-linear Analysis
Wednesday, 29th
of May 2013
When the internal forces are not equal to the externally applied
loads due to the materials nonlinearities, then a nonlinear iterative
procedure is required to update the stiffness matrix of the structure
so as to achieve the equilibrium between the internal and the
external forces. This procedure is known as nonlinear analysis.
7
8.
Non-linear Analysis
Analysis type Short description
Nonlinearity of material Infinitive displacements and deformations
Nonlinear relationship between stress and
strain
Large displacements and rotations but small
deformations
Displacements and rotations are large but
change of the length and angle is small
Linear or nonlinear relation between stress
and strain
Large displacement ,rotation and
deformation
Large change in angle and length
Linear or nonlinear relation strain- stress
Wednesday, 29th
of May 2013
It should be noted that
when we use material
nonlinearity, the
nonlinear response is
solely due to the stress
strain relation.
8
9.
Non-linear Analysis
Wednesday, 29th
of May 2013
Newton-Raphson method:
This method is an iterative procedure where at each iteration the stiffness
matrix of the structure is recalculated and the system of equations is solved
iteratively by setting the incremental loading vector equal to the unbalanced forces,
the stiffness matrix is calculated at every internal iteration based on computed
stress-strain at the previous internal iteration.
9
12.
Wednesday, 29th
of May 2013
The height of the
structure is :44.5 m
12
13.
Results from the Preliminary
Analysis (Linear Static)
ULS Static Linear Analysis
Wednesday, 29th
of May 2013
ULS Static (ACI) =1.2(G) +1.6(Q)
As it can be seen the maximum
developed stresses was 56 MPa. The
deformation were not significant while
our structures initial design is able to
carry the static design loads applied.
13
14.
Results from the Preliminary
Analysis (Linear Static)
Wind Load Linear Analysis
Wednesday, 29th
of May 2013
The maximum stress
developed by wind load
along the x-axis, which has
a value of 5.85 MPa.
14
15.
Results from the Preliminary
Analysis (Linear Static)
The maximum stress
developed due to the wind
load along the y-axis,
which has a value of 11.7
MPa.
Wednesday, 29th
of May 2013
15
16.
Results from the Preliminary
Analysis (Linear Static)
Linear Quasi – Static (Seismic analysis)
Wednesday, 29th
of May 2013
The maximum stress applied
by seismic load on the
horizontal direction, which
has a value of 17.1 MPa.
The code that has been used
for generating the seismic
load was UBC 97.
16
17.
Results from the Preliminary
Analysis (Linear Static)
The corresponding maximum horizontal displacements were found to be equal to
0.77cm and 1.37cm for model wx and wy, respectively. It is evident that the y-
direction is the weak one, thus it results larger displacements Wednesday, 29th
of May 2013
Maximum Story Displacement due to Wind Load
17
18.
Results from the Preliminary
Analysis (Linear Static)
When the seismic load is applied on the structure, for the case of the x-axis the
maximum horizontal displacement was found to be equal to 1.7 cm and in the case
of the y-axis the maximum horizontal displacement was found to be equal 3.53 cm
Wednesday, 29th
of May 2013
Maximum Story Displacement due to Seismic Load
18
19.
Modal Analysis
Deformed shape of Mode 1.
T=1.83 sec
Deformed shape of Mode 2.
T=1.587 sec
Deformed shape of Mode 3.
T=1.043 sec
Wednesday, 29th
of May 2013
19
20.
Computation of the Seismic Load
Wednesday, 29th
of May 2013
Area T(thickness) Self Weight G(dead loads) Q (Live Loads)
Weight From
Loads
Total
Weight M Total
Ground floor 325.2m² 0.1m 796.74kN 5kN 5kN 2113.8kN 57267.3kN 5837.64kg
Mezzanine
floor
325.2m²
0.25m 1991.85kN 5kN 5kN 2113.8kN
1st floor
389.2m²
0.25m 2383.85kN 5kN 2.5kN 2237.9kN
2nd floor- 9th
floor
389.2m²
0.25m 2383.85kN 5kN 2.5kN 2237.9kN
Roof
389.2m²
0.35m 3337.39kN 5kN 7.4kN 2810.024kN
Top Roof
389.2m²
0.25m 2383.85kN 5kN 2.5kN 2237.9kN
20
21.
Our structure was found to have a 1st
fundamental period of 1.83 seconds, thus the
3rd
part of the response spectrum graph will result the required design spectrum
acceleration Sd(T) describes the part of the response spectrum diagram given that
we assume that the structure has a ground type C. According to Eurocode the
factor S =1.15 and Tc =0.6 sec when the ground type is C.
Sd (T) = ag * S*(2.5/q) * ( Tc/T), Vtotal = Sd (T) * M
Total Base Shear: Vtotal = 22.62 MN`
Computation of the Seismic Load
The assumed design acceleration in this case
was assumed to be equal to ag = 0.15g.
According to the response spectrum diagram
of EC8, the design spectrum acceleration is
computed.
Wednesday, 29th
of May 2013
21
22.
Computation of the Seismic Load
Distribution of the Total Base Shear
FLOOR mi zi mi*zi ∑mi*zi (mi*zi)(∑mi*zi)
Horizontal
Load
F1 2910.54kg 1m 2910.54 1419366kg.m 0.00205 47kN
F2 4105.65kg 4.4m 18064.86 0.0127 288kN
F3 4621.75kg 7.8m 36049.65 0.0254 575kN
F4 4621.75kg 11.5m 53150.13 0.0374 846kN
F5 4621.75kg 15.2m 70250.6 0.0495 1120kN
F6 4621.75kg 18.9m 87351.08 0.0615 1392kN
F7 4621.75kg 22.6m 104451.6 0.0735 1663kN
F8 4621.75kg 26.3m 121552 0.08564 1938kN
F9 4621.75kg 30m 138652.5 0.09768 2210kN
F10 4621.75kg 33.7m 155753 0.1097 2482kN
F11 4621.75kg 37.4m 172853.5 0.12178 2755kN
F12 6147.414kg 41.1m 252658.7 0.178 4027kN
F13 4621.75kg 44.5m 205667.9 0.1449 3278kN
Wednesday, 29th
of May 2013
22
23.
∗ Plastic hinges:
Concentrated hinges that were assigned to the frame and shell elements,
which may experience nonlinear behavior.
∗ Layered Shell Elements:
In order to account nonlinearities in all shell finite elements, Area
Properties in SAP2000 were created. These properties were assigned with a
nonlinear layer property.
Nonlinearities and SAP2000
Wednesday, 29th
of May 2013
23
24.
Wednesday, 29th
of May 2013
Deformed shape and the
plastic hinges (step 1).
Deformed shape and
plastic hinges (step 2).
Deformed shape and
plastic hinges (step 3).
Numerical Results (Nonlinear
Analysis)
24
25.
Wednesday, 29th
of May 2013
Deformed shape and
plastic hinges (step 4).
Deformed shape and plastic
hinges prior to failure (front
view).
Deformed shape and plastic
hinges prior to failure (Back
view).
Numerical Results (Nonlinear
Analysis)
25
26.
Numerical Results (Nonlinear
Analysis)
Wednesday, 29th
of May 2013
The first plastic hinges occur for a
total horizontal load of 5.1 MN and
the maximum current capacity of
our structure was found to be 17
MN with a total displacement of
6.1 cm at the top floor.
As it derives from the above curve, the carrying capacity of the structure is not
sufficient in carrying the applied seismic load (22.62MN).
26
27.
Redesign
Wednesday, 29th
of May 2013
The compressive strength of the
concrete is changed to 35 MPa as
opposed to the old 28 MPa. The
modulus of elasticity was
increased also to 33 GPa.
27
28.
Redesign of the Shear Walls
Wednesday, 29th
of May 2013
Section of 35x300 shear
walls were added to
increase the structures
carrying capacity.
28
29.
Redesign
Wednesday, 29th
of May 2013
The rectangular section of
the shear walls at the ground
and mezzanine floors were
changed from section of
40x100 to 30x210.
29
30.
Redesign
Wednesday, 29th
of May 2013
The beams that were added
have a section size of 35x70
cm except the perimetric
beams that had a 20x25 cm
section which was not
modified.
30
31.
Final Modal Analysis
Wednesday, 29th
of May 2013
Deformed shape of Mode 1.
T=1.23 sec
Deformed shape of Mode 2.
T=1.22 sec
Deformed shape of Mode 3.
T=1.1 sec
31
32.
Results of Pushover curve After
Redesign
Wednesday, 29th
of May 2013
The new carrying capacity
of the redesigned frames
was found (22688.135kN)
which satisfies the demand
of EC8.
32
33.
Conclusion
Wednesday, 29th
of May 2013
1- Assessing our structures by using software such as ETABS and SAP2000, is of
significant importance in terms of safety and accuracy. ETABS and SAP2000
automatically generate and assign code-based loading conditions for gravity,
seismic, wind, and thermal forces thus performing the design and assessment
becomes a very efficient procedure.
2- Our numerical results and overall experience showed that modeling RC
structures is a procedure that requires both theoretical knowledge and practical
experience.
33
34.
Conclusion
Wednesday, 29th
of May 2013
3- After performing a modal analysis it was found that the 1st
mode was rotational
thus the geometry of the frame and the stiffness distribution of the shear walls
were irregular. In addition to that, we found that the 1st
fundamental period was
equal to 1.83 seconds that underlines the fact that the flat slab system used derived
a flexible mechanical behavior despite the use of relatively large shear walls.
4- It was found that for the at hand RC structure the controlling design load type is
the seismic load given that the wind loads did not generate larger deformations
and stresses in comparison to those resulted when the seismic loads were
generated and applied. This finding strengthens the rule that says "RC structures
do not suffer in wind loads".
34
35.
Conclusion
Wednesday, 29th
of May 2013
5- In order to perform the pushover analysis we changed the shell FEs used to
model all shear walls with frame elements. This was done so as to overcome the
computational demand issue that resulted when using shell FEs. It was required to
run the nonlinear solver for more than 14 hours when shell FEs were used, so as to
finish a single nonlinear analysis.
6- The 12-storey RC building was found inadequate in carrying the 22.62MN
seismic load according to EC8 according to the numerical results that derived from
the non-linear analysis. For this reason a redesign of the frame was performed so
as to overcome this issue. 35
36.
Conclusion
Wednesday, 29th
of May 2013
7- When the initial frame was reinforced with beams, the mechanical behavior of
the structure changed, while the redesign of the shear walls (add extra shear walls
and increase the thickness of existing shear walls) led to a strengthening of the
carrying capacity of the structure. After applying the redesign, we managed to
increase the carrying capacity according to the code’s demand. In addition to that
the fundamental modes were changed given the normalization procedure of the
stiffness distribution of the initial frame.
8- The procedure of seismic design and assessment of RC structures is much more
complicated than standard design for the static and wind loads through the use of
linear elastic analysis.
36
37.
Thank you for your Attention!
Wednesday, 29th
of May 2013
37
Be the first to comment