An-Najah National University Faculty of Engineering Civil Engineering DepartmentAn-Najah National University
Faculty of Engineering
Civil Engineering Department
1
Introduction:
Al-Nour building is 8 stories reinforced concrete building ,located in Nablus city and used as residential building.
The first story is used as garages with plan area of 700 m^2 and the above 7 stories used as residential apartment (two apartments per floor) with plan area of 490 m^2 due to the setback.
The soil bearing capacity = 400 KN/m2
3
Introduction :
Columns Centers Plan :
Structural System :
The structural system used is on way ribbed slab with load path in x-direction.
Materials:
- Concrete :
- The concrete unit weight = 25 (KN/m3).
- Reinforcing Steel: The yield strength of steel is equal to 4200 Kg/cm2 (420 MPa).
-Others :
Material
Superimposed dead load = 4.5 KN/m2
Partition load = 1 KN/m2 .
- Live load = 2 KN/m2 .
- Seismic loads : shown later.
- The following are the design codes used :
ACI – code 2008 .
Wu = 1.4DL.
We performed a preliminary design for all structural elements conceptually.
The story height is 3.12 m.
The following are the preliminary dimensions :
Slab :
- web width = 12 cm.
- Ultimate load = 14.06KN/m².
Beams :
Since the structural system is one way ribbed slab (load path in x-direction) we have :
Main beams in y-direction : 30x60 cm.
Secondary beams in x-direction : 40x25 cm.
Columns :
Area carried by column = 28 m2
Ultimate slab load = 14.06KN/m²
Pu = 3769.6 KN.
Ag = 2326.9 cm2.
Footing :
we performed an preliminary design for footing of the previous column as single footing.
with dimensions of 2.9x2.7x0.7 m.
Chapter 3 : Static Design
Area sections dimensions :
Area section name
Static design:
Verification Of SAP model:
We perform the verification for SAP models( one and eight stories and it was OK) the following is verification for eight stories :
1. Compatibility satisfied :
Taking beam C in second story (taking 8 m span) :
Load type
Hand results(KN)
So the slab deflection = 7.16mm < allowable long term def. OK.
2. Design for shear :
shear per rib = 0.55*36.75 = 20.2 KN.
So 23.2 ≥ 20.2 OK
Static Design :
The moments are read from SAP using section cut :
Point location/term
Taking a sample beam (beam B in the first floor) :
- The beam section dimensions are :
- Total depth (h) = 700 mm.
- The effective depth (d) = 650 mm.
-Beam width (bw) = 400 mm.
- min reinforcement ratio = 0.0033.
- φVc = 159.1 KN.
The following are the values of min reinforcement:
(As) min = 0.0033*b*d=0.0033*400*210= 277.2 mm (3Φ12).
Vc = 0.75*0.167**400*210/1000= 68.58KN.
Static Design :
Design information :
 Floor no.
4774
C3
16φ20
From the graph
= 81.66 >22Column is long.
Mc = ns*M2 = 1.67(153.1) = 255 KN.m
From the interaction diagram:
As =0.01xAg =0.01x40x80 =3200mm2
Same as SAP value.
Use 412mm bottom steel.
Use 412mm top steel.
Vc = 80.83KN.
Footing design
Single footing:
Is one of the most economical types of footing and is used when columns are spaced at relatively long distances .
Bearing capacity of the soil=400 KN/m2.
Footing grouping
Group Name
Distribution in each direction
Wu=1.2(5+3.9) +1.6(5) =18.68KN/m2.
Verification of SAP model:
- Importance factor (I) = 1 .
- Area mass = 0.458 ton/m2
- Soil class = Class B.
- Spectral accelerations : Ss = 0.5 .
R = 4.5 in y-direction.
Mode No.
Dynamic Design:
Mode No.
We will perform the dynamic design using response spectrum method:
Define two response spectrum load cases one in x-direction and the another in y-direction :
- For response-x: * Scale factor = 3.27.
*Scale factor = 0.654.
*Scale factor = 0.981.
Perform design using envelope combination and check whether static or dynamic combination controls .
Slab design :
- Reinforcement from envelope combination:
- Reinforcement from envelope combination is considered since the dimensions are increased:
Dynamic design Controls
Design of columns :
Interior column B3.
Edge column B2.
Corner column A4 .
The comparison is performed and static design controls for all columns.
The following table shows the comparison for column B3 :
Dynamic Design :
Static design OK for columns.
The following table shows the comparison for column B3 (M3, V2 ):
Chapter 5 : Structural Modeling Of One Way Ribbed Slab
Structural Modeling Of One Way Ribbed Slabs
The ribbed slabs can be represented by one of the following ways :
Equivalent stiffness method : find the equivalent thickness of a solid slab that can achieve the same rib stiffness.
Represent it as separate ribs (T-section).
Represent the ribs by rectangular ribs and flange.
The main objective is to prove that three models give the nearly the same results.
Structural Modeling Of One Way Ribbed Slabs
Model 1 : Equivalent stiffness method :
Equivalent slab thickness (t) = 19.45 cm.
I T-sec = I rec →( 0.55*h3eq /12) = 3.371*10-4
h3eq = 19.45 cm.
- Stiffness modifiers :
M11 = 0.35 .
M22 = 0.0244
M1-2 = 0.0244.
Model 2 : Representation as separate ribs :
- Stiffness modifiers :
Loads on ribs.
Structural Modeling Of One Way Ribbed Slabs
Model 3 : the slab is represented as rectangular ribs and flange.
1. The rectangle section should satisfy
The actual T-section.
2. Stiffness modifiers :
I 3-3 = 0.6 .
8 cm
25 cm
55 cm
15 cm
All the previous models are verified according to manual solution.
Static analysis is performed for the three models and we read the moment and shear at point C3 in span C3-4 for beam C in the second floor :
load
Structural Modeling Of One Way Ribbed Slabs
also dynamic analysis and design performed for the three models and the following are the modal information :
Mode
Direction
Period
MMPR
Model 1 :
Also the same span taken in the beam C and the following are the values of moment and shear from envelope combination :
Structural Modeling Of One Way Ribbed Slabs
Point
Final conclusion :
from the previous data shown in tables we note that all the three models give near results.
So, we can represent the slab model by any of the previous models but perform the changes in loads assignment and stiffness modifiers.
Thanks for your attention