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**3D Dynamic Design Of AL-Nour Building**

An-Najah National University Faculty of Engineering Civil Engineering Department 3D Dynamic Design Of AL-Nour Building Prepared by: 1. Ahmad Rashdan. 2. Jaffar Hassan . 3. Mustafa Aqra. 4. Odai Odeh. Supervised by: Dr. Abdul Razzaq Touqan

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**Chapter 1 : Introduction**

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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

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**Introduction : The Following slides shows : 1. columns centers plan.**

2. 3D model of the building.

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Columns Centers Plan :

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Structural System : The structural system used is on way ribbed slab with load path in x-direction.

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**Materials: - Concrete : - f’c= 320 kg/cm²( 32 MPa) For columns.**

- f’c= 240 kg/cm²( 24 MPa) for others. - The concrete unit weight = 25 (KN/m3). - Reinforcing Steel: The yield strength of steel is equal to 4200 Kg/cm2 (420 MPa). -Others : Material Unit weight (KN/m3) Reinforced concrete 25 Plain concrete 23 Sand 18 Aggregate 17 Y-tong 5 Blocks 12 Polystyrene 0.3 Masonry stone 27 Light weight block 6 Tile 26

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**Design loads : - Dead loads in addition to slab own weight :**

Superimposed dead load = 4.5 KN/m2 Partition load = 1 KN/m2 . Masonry wall weight = KN/m. - Live load = 2 KN/m2 . -Water tanks load = 1.14 KN/m2 - Seismic loads : shown later.

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**Design codes and load combinations:**

- The following are the design codes used : ACI – code IBC ASCE for design loads. The following are the load combinations used : Wu = 1.4DL. Wu = 1.2DL + 1.6LL . Wu = 1.2DL + LL ± E. Wu = 0.9DL ± E

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**Chapter 2 : Preliminary Design**

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**Preliminary design The story height is 3.12 m.**

We performed a preliminary design for all structural elements conceptually. The story height is 3.12 m. The following are the preliminary dimensions : Slab : - depth = 25 cm (based on deflection criteria) . - web width = 12 cm. - slab own weight = 4.55KN/m². - Ultimate load = 14.06KN/m².

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**Preliminary Design 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 : Take a sample columns ( B3) : Area carried by column = 28 m2 Ultimate slab load = 14.06KN/m² Pu = KN. Ag = cm2. → Use columns of 40x60cm2.

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**Preliminary design and checks**

Footing : we performed an preliminary design for footing of the previous column as single footing. with dimensions of 2.9x2.7x0.7 m.

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**Chapter 3 : Static Design**

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**Static design : Final dimensions : 1. frame sections : Member**

Depth(cm) Width(cm) Col. 80 40 Main interior beams 70 Main exterior beams 75 30 Secondary beams 25 Tie beams 50

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**Equivalent Slab thickness**

Static Design: The new web width (bw) = 15 cm. Area sections dimensions : Area section name Thickness (cm) Actual Slab 25 Equivalent Slab thickness 19.45 (in SAP model) Shear wall 30 (initially) The story height = 3.5 m

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**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 :

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**Static Design 2.Equilibrium Satisfied :**

Load type Hand results(KN) SAP results (KN) Error % Dead load 0.01 Live load 3.Stress -Strain relationship satisfied: Taking beam C in second story (taking 8 m span) : Load` M-ve (left)(KN.m) M+ve (KN.m) M-ve(right) Total moment (KN.m) SAP Result 325.13 208.63 371.41 556.9 1D Result 341.40 433.61 558.21 Error 2.3%

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**Static Design : Slab design : 1. Check slab deflection :**

So, ∆dead = 2.92 mm. ∆Live = 0.78mm. Δ long term = 7.16mm. The allowable deflection = 4000 /240 = mm. So the slab deflection = 7.16mm < allowable long term def. OK. 2. Design for shear : The rib shear strength = 23.2KN. The max shear = KN/m. shear per rib = 0.55*36.75 = 20.2 KN. So 23.2 ≥ OK So the slab is Ok for shear.

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**Static Design : 3. Design for bending moment :**

The moments are read from SAP using section cut : Point location/term Moment(KN.m) As(mm2) Bars A1 6.3 113 2 Φ 12 A1- B1 8.6 2 Φ 10 B1 10.48 125 B1- C1 7.25 C1 10.29 122 C1 – D1 8.1 D1 9 D1 – E1 E1 13.55 163.3

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**Static Design : Design of beams in y-direction :**

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 = - As min = ρbd = *400*650 = 858 mm2 - φVc = KN. - (Av/s)min =

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**Static Design : - Design information : point As(mm) As min (Av/s)**

(Av/s) min PI(m) Length(m) bars stirrups B1 700 858 0.333 0.6 2 5Φ16 cm B1-2 854 -- 5.9 B2(L) 1676 1.3 4.8 6φ20 B2(R) 0.55 1.5 cm B2-3 1044 _ 7.9 B3(L) 1581 0.48 cm B3(R) B3-4 772 B4 1 2.3

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**Static Design : Design of secondary beams:**

Total depth(H) = 25cm.(hidden beam) d= 21cm (cover =4cm) Width = 40cm. The following are the values of min reinforcement: (As) min = *b*d=0.0033*400*210= mm (3Φ12). Vc = 0.75*0.167**400*210/1000= 68.58KN.

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**Static Design : Design information : Point As(mm) As min (mm) (Av/s)**

(Av/s)min PI(m) bars stirrups A4 469 277.2 0.333 0.88 5Φ12 A4-B4 277 3Φ12 B4 429 4Φ12 B4-C4 259 C4 424 C4-D4 260 D4 425 D4-E4 265 E4 432 E4-F4 147 F4

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**Design of columns: Column grouping, Area of steel& stirrups: Floor no.**

As(mm2) column group Distribution of steel Stirrups spacing (mm) All floors except No.8 All Columns 3200 C1 16φ16 mm Floor No.8 D2 & G2 3766 C2 20φ16 mm A2, B2, C2, H2, I2 & J2 4774 C3 16φ20

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**Manual design Pu=3034.75KN MY = 11.02 KN.m(maximum value)**

Check slenderness ratio for corner column C.A-1 From the graph K = 3.5 𝐾 𝐿 𝑢 rx = 3.5x x0.8 = >22 ⟹Column is long. 𝐾 𝐿 𝑢 ry = 3.5x x0.4 = >22 ⟹Column is long. Pu= KN MY = KN.m(maximum value) MX = KN.m( maximum value) Mc = ns*M2 = 1.67(153.1) = 255 KN.m From the interaction diagram: ≤1% use minimum steel ratio use =1%. As =0.01xAg =0.01x40x80 =3200mm2 Same as SAP value.

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**Tie beam design Minimum area of steel = 0.0033*b*d =436 mm2.**

Use 4Ф12mm bottom steel. Use 4Ф12mm top steel. Shear design : Vu at distance (d = 44cm) = 16.35KN, ФVc = 80.83KN. Use 1Ф8

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**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.

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**Footing grouping Group Name Columns Service load(KN)**

Ultimate load (KN) F1 A1, B1,C1,D1,E1,F1,G1,H1,I1,J1 305.6 375.7 F2 A2, J2,A4 B4,C4,D4,G4,H4,I4,J4, F3 B2,C2, D2,G2,H2,I2,A3,B3,C3,D3,G3,H3, I3,J3 Combined E4 & F4 Footing grouping according to column’s ultimate load.

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**Steel distribution/m’ Area of shrinkage steel**

footing details Group Area of footing (m2) Dimensions (m) Depth Steel distribution/m’ (Both directions) Area of shrinkage steel (mm2) Distribution in each direction F1 0.96 1.2x0.8 0.3 4 Ø 14mm no No F2 6.21 2.7x2.3 0.55 5 Ø 18mm 𝟓𝟖𝟓 1 Ø F3 9.57 3.3x2.9 0.75 6 Ø 18mm 𝟔𝟕𝟓 1 Ø Combined 13.11 5.7x2.3 1Ø25 /200mm 778.2

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**Design of Stairs h min = 𝑙 20 =0.187m⇒Use h=0.20m.**

Own Weight=0.2x25=5KN/m2. Live load = 5KN/m2. Superimposed loads =2.14 KN/m2 Superimposed loads of extra of stairs=1.76 KN/m2 Wu=1.2(5+3.9) +1.6(5) =18.68KN/m2. Ø𝑉𝑐=110.23KN>𝑉𝑢=20.82𝐾𝑁

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**Verification of SAP model:**

Compatibility: “Compatibility Satisfied”

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**Total moment( 𝐖 𝐥 𝟐 𝟖 ) (KN.m)**

Cont. Equilibrium: Load type Hand results(KN) SAP results(KN) Error % Dead load 293.04 292.82 0.08 Live load 181.24 181.12 0.07 “Equilibrium Satisfied” Stress-Strain Relationships: Load M-ve(left) (KN.m) M+ve M-ve(right) Total moment( 𝐖 𝐥 𝟐 𝟖 ) (KN.m) 3D SAP Result 22.1 11.9 19.46 32.68 1D Result 21.72 10.86 32.58 Error 0.3% “Stress–strain relationship satisfied” M=22.1 KN.m/m 𝜌= 𝐴 𝑠 =331 𝑚𝑚 2 /m. 𝐴 𝑠 𝑚𝑖𝑛 = 𝜌 𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑏ℎ=360 𝑚𝑚 2 > 𝐴 𝑠 ⇒ 𝑢𝑠𝑒 1∅12/250𝑚𝑚 𝑖𝑛 𝑎𝑙𝑙 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛𝑠.

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**Chapter 4 : Dynamic Design**

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**Dynamic Design: Methods for dynamic analysis:**

Equivalent static method. Time history method. Response spectrum analysis. Input parameters in dynamic analysis : - Importance factor (I) = 1 . - Peak ground acceleration (PGA) = 0.2g . - Area mass = ton/m2 - Soil class = Class B. - Spectral accelerations : Ss = 0.5 . S1 = 0.2 . - response modification factor R = 3 in x-direction. R = 4.5 in y-direction.

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**Dynamic Design : Modal information :**

- For eight stories before enlarging beams in x-direction : Mode No. Direction Period (sec.) MMPR % 1 X 2.55 77 2 RZ(Torsion) 1.707 67 4 y 0.972 65 - Enlarge the beams 2 &4 to 30x70 (width*depth)

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Dynamic Design: - For eight stories after enlarging beams in x-direction : Mode No. Direction Period (sec.) MMPR % 1 X 1.58 80 2 RZ(Torsion) 1.5 64 3 Y 0.795 65.4 4 0.497 11 - Comparison with manual results : Mode direction SAP result(sec) Manual result(sec) Error % x- direction 1.58 1.45 8 % y- direction 0.795 0.73

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**Dynamic Design : Response spectrum analysis :**

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 = - For response-y: * Scale factor = 2.18. *Scale factor = Perform design using envelope combination and check whether static or dynamic combination controls .

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**Static design controls**

Dynamic Design : Slab design : The comparison is performed. Static design controls

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**Static design Controls**

Dynamic Design : Design of beams in y-direction : - Reinforcement from envelope combination: - Reinforcement from static combination: Static design Controls

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**Dynamic design Controls**

Design of beams in X-direction : - Reinforcement from envelope combination is considered since the dimensions are increased: Dynamic design Controls

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**Dynamic Design : Design of columns :**

Three representative columns are selected : 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 :

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**Static design OK for columns.**

Dynamic Design : The following table shows the comparison for column B3 (M3, V2 ): floor/term Envelope combination Static combination moment shear axial As(mm2) 1 68.04 31.34 3200 5.54 1.678 4553.3 2 45.78 22.15 6.97 3.7 3982.2 3 49.81 22.82 4.78 2.73 3409.1 4 47.33 20.07 4.62 2.55 2841.9 5 44.51 18.49 2277.7 3.78 2.12 1716.5 6 42.58 16.78 3.71 2 1699.8 7 39.19 13.98 1156.2 2.88 1.36 8 26.75 6.82 3.18 603.8 Static design OK for columns.

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**Chapter 5 : Structural Modeling Of One Way Ribbed Slab**

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**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.

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**Structural Modeling Of One Way Ribbed Slabs**

Model 1 : Equivalent stiffness method : Equivalent slab thickness (t) = cm. I T-sec = I rec →( 0.55*h3eq /12) = 3.371*10-4 h3eq = cm. γeq = KN/m^ to achieve the same weight. - Stiffness modifiers : M11 = M22 = M1-2 =

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**Structural Modeling Of One Way Ribbed Slabs**

Model 2 : Representation as separate ribs : - Stiffness modifiers : I 3-3 = I 2-2 = Torsional constant(J)= The loads are inserted as line Loads on ribs. Substitute the weight of blocks.

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**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 . I2-2 = 0.6 . J = 3. Weight modifier = Flange Modifiers : - M11 = (almost zero). - M 22 = - M 1-2 = (almost zero). → we have to substitute the weight of blocks. 55 cm 8 cm 25 cm 15 cm

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**Structural Modeling Of One Way Ribbed Slabs**

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 Moment (KN.m) Shear (KN) (mm2) ( (mm2/mm) SAP Model 1 Results 371.41 268.63 1615 0.545 SAP Model 2 Results 377.87 286.43 1645.1 0.634 SAP Model 3 Results 373.56 274.13 1625 0.573

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**Structural Modeling Of One Way Ribbed Slabs**

also dynamic analysis and design performed for the three models and the following are the modal information : Model 1 : Mode Direction Period MMPR Mode 1 x-direction 1.581 80 Mode 2 Torsion(Rz) 1.503 64 Mode 3 y- direction 0.796 65.4 Model 2 : Mode Direction Period MMPR Mode 1 x-direction 1.622 77.0 Mode 2 Torsion(Rz) 1.555 79.5 Mode 3 y- direction 0.924 70.9 Model 3 : Mode Direction Period MMPR Mode 1 x-direction 1.542 80.3 Mode 2 Torsion(Rz) 1.456 65.5 Mode 3 y- direction 0.769 65.7

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**Structural Modeling Of One Way Ribbed Slabs**

Also the same span taken in the beam C and the following are the values of moment and shear from envelope combination : Model 1 : Point Envelope combination moment shear As(mm2) Av/s (mm2/mm) C2 316.0 243.7 1359.4 0.422 C2-C3 208.6 16.3 1053 C3 371.1 268.5 1613 0.545 Model 2 : Point Envelope combination moment shear As(mm2) Av/s (mm2/mm) C2 329.7 259.6 1422 0.5 C2-C3 211.0 17.7 899.1 C3 377.9 286.4 1645 0.634 Model3: Point Envelope combination moment shear As(mm2) Av/s (mm2/mm) C2 317.6 243.0 1367 0.418 C2-C3 209.1 16.2 891.3 C3 373.6 274.1 1625 0.573

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**Structural Modeling Of One Way Ribbed Slabs**

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.

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**Thanks for your attention**

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