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GH ASACHI TECHNICAL UNIVERSITY OF IASI FACULTY OF CIVIL ENGINEERING AND BUILDING SERVICES Profile: CIVIL ENGINEERING Specialization: CIVIL ENGINEERING-TRAINING Qualification: Bachelor Engineer Year of study: 3nd year Education Form: Day Courses Academic year: 2013-2014
Civil constructions IIProject
Student: Mirodone MadalinGroup: 3308
Project theme The project consists in the design of a multy-storey building, having one of the following destinations: 1. Block of flats2. Students acomodation hostel3. Hotel The building has UG+G+ 4Fl, meaning that has an underground floor, ground floor and 4 floors.The envelope of the building consists of:- load-bearing walls of reinforced concrete or non load-bearing walls of hollow brick or cellular concrete block masonry protected on the external face with al layer of efficient thermo insulating materials (fireproofed expanded polystyrene for face wall, mineral wool rigid plates, extruded polystyrene etc.);- ventilated or un-ventilated could (insulated) terrace roof;- the ground floor plate over unheated basement will be insulated on the ceiling of the basement;- the doors and windows can be of multi-layer wood or PVC profiles with thermal insulating double or triple glassed window panels with Low CTE float glass. The windows will be provided with ventilating systems or with three opening positions in order to provide an adequate thermal protection and natural ventilation of the indoor space.The structure will have:1. Pedestrian or non-pedestrian reinforced concrete flat roof;2. Monolithic or precast reinforced concrete shear walls mixed with lamellar frames;3. Reinforced concrete stairs;4. Elastic cross beams.
It is situated in the urban area, Brasov, having acces to all the city facilities: water supply, electricity, internet connection, connection to the sewerage infrastructure, acces roads and other public services.The project must contain information and details about:- the type and the composition of structural and for envelope elements ( walls, columns, floors, foundations, and roof);- the joints of the main structural and for envelope elements;- the heat conservation capacity of the building;- the structural performance under the load combination that contain dead, snow, live loads and seismic action.The thermal and structural design and the constructive details of the elements already mentioned.
The slope of the terrain is about 2%.The project content : A. Written part: Project theme; Project content; Technical report; The design of the walls and roof for the hygrothermal conditions; The assesment of loads and design load combination; The computation of the shear walls sectional characteristics; Stress and strains analysis for the cross shear walls;B. Drawings: Current floor plan scale: 1/50; Groundfloor plan scale: 1/50; Cross section through the staircase scale: 1/50; Roof plan scale: 1/100; Consructive details scale: 1/10;
Thermal insulation design In order to obtain the thickness of the insulation layer a series of operations and computation are needed. The unidirectional specific thermal rezistance of a building element is calculated by the formula: [].Where: d-thickness of the layer- the thermal conductivity of the material The thermal rezistance of each element of the building envelope will be compared with the minimum thermal rezistance (). The following condition has to be imposed: and Exterior wallsFor reinforced concrete wall:OUTER WALL
No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,125
2Lime plaster0,030,870,0344828
3R.C. Wall0,21,620,1234568
4Rigid mineral woolX0,050
5Cement plaster0,0150,930,016129
61/2--0,042
Total thermal rezistance of the element R=0,3410686
R.M.W insulation board with basalt fibers type PB 160
For exterior walls the is 1,80. It results that 2,16[]. if , it results that ...... X>0,09 m 10cm thick of insulated layer.The thickness of the insulation layer for the outer wall made of reinforced concrete will be equal to 10 cm.No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
1/i--0,125
1Lime plaster0,030,870,0344828
2R.C. Wall0,21,620,1234568
3Rigid mineral wool0,10,052
4Cement plaster0,0150,930,016129
1/2--0,042
Total thermal rezistance of the element R=2,3410686
For masonry wall:No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,125
2Lime plaster0,030,870,0344828
3Masonry brick wall0,20,300,6666667
4Rigid mineral woolX0,050
5Cement plaster0,0150,930,016129
61/2--0,042
Total thermal rezistance of the element R=0,8842785
if , it results that []. X>0,06m.The thickness of the insulation layer for the outer wall made of masonry will be equal to 10 cm.
No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,125
2Lime plaster0,030,870,0344828
3Masonry wall(BCA)0,20,300,6666667
4Rigid mineral wool0,10,052
5Cement plaster0,0150,930,016129
61/2--0,042
Total thermal rezistance of the element R=2,8842785
Plate over the unheated basementcold flooring
No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,167
2Ceramic tiles0,0152,030,0073892
3Mortar bead0,030,930,0322581
4R.C. Slab0,151,620,0925926
5Rigid mineral woolX0,050
6Ceiling plaster0,0150,180,0833333
71/2--0,084
Total thermal rezistance of the element R=0,4665732
For plate over the basement the is 2,90. It results that 3,48 [].if , it results that []. X>0,1506 m.The thickness of the insulation layer for the floor over the unheated basement will be equal to 18 cm.No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,167
2Ceramic tiles0,0152,030,0073892
3Mortar bead0,030,930,0322581
4R.C. Slab0,151,620,0925926
5Rigid mineral wool0,180,053,6
6Ceiling plaster0,0150,180,0833333
71/2--0,084
Total thermal rezistance of the element R=4,0665732
Terrace roofFor terrace roof the is 5,00 . It results that 6 [].No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,167
2Ceiling plaster0,0150,180,0833333
3R.C. Slab0,151,620,0925926
4Sloping layer0,050,930,0537634
5Water vapour barrier0,0020,380,0052632
6Extruded polystyreneX0,0330
7Waterproof layer0,0030,380,0078947
8Protecting layer(bitumen)0,050,170,2941176
91/2--0,084
Total thermal rezistance of the element R=0,4400838
W.V.B and W.L. Are -- PVC carpet with =1800 kg/ m3
if , it results that []. X>0,18 m.The thickness of the insulation layer for the terrace roof will be equal to 20 cm.No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,167
2Ceiling plaster0,0150,180,083333
3R.C. Slab0,151,620,092593
4Sloping layer0,050,930,053763
5Water vapour barrier0,0020,380,005263
6Extruded polystyrene0,20,0336,060606
7Waterproof layer0,0030,380,007895
8Protecting layer(bitumen)0,050,170,294118
91/2--0,084
Total thermal rezistance of the element R=6,848571
Thermal bridges identification The computations and the analysis of the thermal bridges are done in a tabular form. A tabel where the envelope elements and there area is presented below:
Envelope's elements nameEnvelope's elements surface [sqm]Total [sqm]
NSEV
Exterior wallsMasonryground floor55,4655,4636,2236,22737,8
1-4 floors221,84221,84146,88146,88
Windowsground floor4,644,34,324,3270,64
1-4 floors18,7617,3217,2817,28
Doorsground floor7,141,680026,6
1-4 floors17.228,400
Inferior plate [A1]241,4241,4
Superior plate [A2]241,4241,4
Envelope's surface1317,24
Facade surface [sqm]257.8247.5164.16164.16
A tabel with necessary information about the volume of the building is shown:
Heated volume
V=A(Hstorey*nost-hslab)
Groundfloor1..4 Floors
A [sqm]241.4241.4
H [m]2,811,20
hslab [m]0,150,15
V [cm3]675.9
Vtotal [m3]2703.68
No.Building elementBridge detailHeat loss ()Thermal bridge length (l) x l
W/mKmW/K
123456
1.North faade
Outer corner0,06281,68
Walls intersection0,04562,24
0,06563,36
Attic0,1419,42,716
Current floor0,0973,66,624
0,173,67,36
Basement0,1519,42,96
1.South faade
Outer corner0,06281,68
Walls intersection0,04562,24
0,06563,36
Attic0,1419,42,576
Current floor0,0943,23,888
0,1143,24,752
Current floor & balcony0,2130,46,384
0,1530,44,56
Basement0,1519,42,76
1.East faade
Outer corner0,1282,8
Walls intersection0,14283,92
Attic0,1511,41,71
Current floor0,1145,65,016
0,1345,65,928
Basement0,1811,22,016
1.West faade
Outer corner0,1282,8
Walls intersection0,14283,92
Attic0,1511,41,71
Current floor0,1145,65,016
0,1345,65,928
Basement0,1811,22,016
2.Floor over the basementBasement0,2536,89,2
0,1181,68,976
0,2722,46,048
3.Terrace roofAttic0,1836,86,624
0,1922,44,256
4.OpeningsCarpentry S0,27193,452,218
Carpentry E0,276016,2
Carpentry N0,2711631,32
Carpentry V0,276016,2
Area (A)Thermal resistance (R)(xl)Corrected thermal resistance (R'j)Temp. corr. Factor ()R'mA x / R'm
m^2m^2k/wW/Km^2k/w-m2/WW/K
78910111213
221,842,8827,3362,1688455711,9395669123,7905
221,842,8832,22,000511071108,7562
146,882,3421,391,75307162177,07906
146,882,3421,391,75307162177,07906
206,084,0624,2242,74837020,5382,748370240,34065
206,086,8410,885,0252806415,025280641,00865
115,9380,710,7165,6257
633,6799
The general factor of thermal insulation G
This factor of thermal insulation reflects the sum of all thermal loss trough all the building envelope elements for a thermal difference of 1 Kelvin () plus the losses because of ventilation and air infiltration.
GGN [W/m3K];
n=0,5
V=2668,2923[m^3]
G=0,4074852[W/m^3K]
A=1162,24[m^2}
V=2668,2923[m^3]
A/V0,4355745m^2/m^3
GN=0,42
Evaluation of the condensation risk
Datas for Brasov, climatic zone IV: - Ti=+20 C; - Te= -21 C; - Te, med= +7.5 C; - i= 60% ; e= 70%
1. Establishing of the temperature variation in the structure of the element:
a) reinforced concrete wallNo.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,125
2Lime plaster0,030,870,0344828
3R.C. Wall0,21,620,1234568
4Rigid mineral wool0,10,052
5Cement plaster0,0150,930,016129
61/e--0,042
Total thermal rezistance of the element R=2,3410686
Tsi= 19,33
T2= 19,14 T3= 18,48T4= 7,81 T5= 7,72
b) masonry wall
No.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,125
2Lime plaster0,030,870,0344828
3Masonry wall(BCA)0,20,300,6666667
4Rigid mineral wool0,10,052
5Cement plaster0,0150,930,016129
61/2--0,042
Total thermal rezistance of the element R=2,8842785
Masonry wall(BCA) -- autoclaved concrete blocks with usual joints, type GBN 30
Tsi= 19,45 T2= 19,30 T3= 16,42 T4= 7,75 T5= 7,68
c) terrace roofNo.Material layerLayer thickness [m]Thermal conductivity ()[W/mK]d/
11/i--0,167
2Ceiling plaster0,0150,180,083333
3R.C. Slab0,151,620,092593
4Sloping layer0,050,930,053763
5Water vapour barrier0,0020,380,005263
6Extruded polystyrene0,20,0336,060606
7Waterproof layer0,0030,380,007895
8Protecting layer(bitumen)0,050,170,294118
91/2--0,084
Total thermal rezistance of the element R=6,848571
Tsi= 19,69 T5= 19,26 T2= 19,54 T6= 8,20 T3= 19,37 T7= 8,19 T4= 19,27 T8= 7,65
2. The determination of the saturated vapour pressure of the inside and outside air (pse,psi) and the saturated vapour pressure on each surface ( ps,si,ps1, ...ps,se).psi=2340 [Pa]; pse= 1038 [Pa].a) Reinforced concrete wallTsi= 19,33 ps,si = 2240 [Pa]
T2= 19,14ps2 = 2211 [Pa]T3= 18,48 ps3 = 2118 [Pa]T4= 7,81 ps4= 1059 [Pa]T5= 7,72 ps5 = 1051 [Pa]b) Masonry wallTsi= 19,45 ps,si= 2251 [Pa]T2= 19,3 ps2= 2240 [Pa]T3= 16,42 - ps3= 1865 [Pa]T4= -7,75 ps4= 1051 [Pa]T5= 7,68 ps5= 1044 [Pa]c) Terrace roof
Tsi= 19,69 ps,si= 2282 [Pa]; T5= 19,26 ps5= 2226 [Pa];T2= 19,54 ps2= 2267 [Pa]; T6= 8,20 ps6= 1088 [Pa];T3= 19,37 ps3= 2240 [Pa]; T7= 8,19 ps7= 1081 [Pa];T4= 19,27 ps4= 2226 [Pa]; T8= 7,65 ps8= 1044 [Pa].
3. The determination of outside and inside air water vapours partial pressure: pve , pvi. [Pa]. pvi= 1404 [Pa]; pve= 726.6 [Pa].4. Computation of the vapour resistivity of each material. Mj= ; .a) Reinforced concrete wallMaterial layerThicknessMj1/KdRv
Lime plaster0,0354000000005,3858600000
R.C: wall0,2540000000021,32,3E+10
R.M.W.0,154000000002,51,35E+09
Cement plaster0,01554000000007,1575100000
Rv,2== 8,58* 108 m/s Rv,3= 2,3*1010 m/s;Rv,4= 1,35*109 m/s;Rv,5= 5,75*108 m/s.b) Masonry wallMaterial layerThicknessMj1/KdRv
Lime plaster0,0354000000005,3858600000
Masonry0,254000000004,34,644E+09
R.M.W.0,154000000002,51,35E+09
Cement plaster0,01554000000007,1575100000
Rv,2= 8,58*108 m/s;Rv,3= 4,644* 109 m/s;Rv,4= 1,35*109 m/s;Rv,5= 5,75*108 m/s.c) Terrace roofMaterial layerLayer thickness [m]Mj1/KdRv
Ceiling plaster0,01554000000001,7137700000
R.C. Slab0,15540000000021,31,7253E+10
Sloping layer0,0554000000007,11917000000
Water vapour barrier0,002540000000000
Extruded polystyrene0,25400000000121,296E+10
Waterproof layer0,003540000000000
Protecting layer(bitumen)0,05540000000000
Rv,2= 13,77*107 m/s Rv,5=--- Rv,3= 1,725*1010 m/s Rv,6=1,296*1010 m/sRv,4= 19,17* 108 m/s Rv,7=--- Rv,8=---
5. `Graphical representation of the building element.
6. Graphical representation of partial and saturated pressures diagrams.
Loads evaluationPermanent loads-given by the self weight of the building elements1) The self weight of the outer wall made of reinforced concrete:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]
1Lime plaster0,0317000510688,5
2R.C. Wall0,22400048006480
3Rigid mineral wool0,11600160216
4Cement plaster0,01518000270364,5
Self-weight on sq m of the element57407749
2) The self weight of the outer wall made of masonry:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]
1Lime plaster0,0317000510688,5
2Masonry wall(BCA)0,2825016502227,5
3Rigid mineral wool0,11600160216
4Cement plaster0,01518000270364,5
Self-weight on sq m of the element25903496,5
3) The self weight the inner wall made of reinforced concrete:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]
1Lime plaster0,0317000510688,5
2R.C.0,22400048006480
3Lime plaster0,0317000510688,5
Self-weight on sq m of the element58207857
4) The self weight of the inner wall made of masonry:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]
1Lime plaster0,0317000510688,5
2Masonry0,2825016502227,5
3Lime plaster0,0317000510688,5
Self-weight on sq m of the element26703604,5
5) The self weight of the terrace roof:
No.Material layerLayer thickness [m]Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]
1Ceiling plaster0,015500075101,25
2R.C. Slab0,152400036004860
3Sloping layer0,05180009001215
4Water vapour barrier0,002915018,324,705
5Extruded polystyrene0,2960019202592
6Waterproof layer0,003915027,4537,0575
7Protect layer(bitumen)0,0511000550742,5
Self-weight on sq m of the element7090,759572,513
6) the self weight of the current floor with cold finishing:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
01/i[m][N/m^3][N/m^2]1,35[N/m^2]
1Ceramic tiles0,01524000360486
2Mortar bead0,0318000540729
3R.C. Slab0,152400036004860
4Rigid mineral wool0,181600288388,8
5Ceiling plaster0,015500075101,25
Self-weight on sq m of the element48636565,05
7) the self weight of the current floor with warm finishing:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
01/i[m][N/m^3][N/m^2]1,35[N/m^2]
1Parquet0,0160006081
2Mortar bead0,0318000540729
3R.C. Slab0,152400036004860
4Rigid mineral wool0,21600320432
5Ceiling plaster0,015500075101,25
Self-weight on sq m of the element45956203,25
8) The self weight of the stairs:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]
1Finishing( ceramic tiles)0,01524000360486
2Mortar bead0,0218000360486
3R.C. Slab0,22400048006480
4Ceiling plaster0,015500075101,25
Self-weight on sq m of the element55957553,25
Variable loads1) The self weight of the dividing walls:No.Material layerLayer thickness Specific weight (xg)Characteristic load (gk) fDesign load (gd)
0-[m][N/m^3][N/m^2]1,35[N/m^2]hwall
1Lime plaster0,0051700085114,752,8
2Gypsum board0,04811000528712,8
3Mineral wool0,086004864,8
4Lime plaster0,0051700085114,75
Self-weight on sq m of the element7461007,1N/m^2
the weight of the wall Gk281,988daN/m^2100,71daN/m^2
The equivalent uniform distrib load100daN/m^2
Live loadsImposed loads on buildings, arising from occupancy.
Category of loaded area A: Categories of laoded areasqk [KN/sqm]
floors1,5
stairs3
balconies2,5
not accessible roofs0,75
accesible roofs1,5
Snow loadsSnow loads
Sk=*Ce*Ct*s0,k
s0,k=2 [KN/m2]
=0.8
Ce=1
Sk=1.92 [KN/m2]
Where: - is the shape coefficient; Ce is the exposure coefficient; Ct is the thermal factor; S0,k is the characteristic value of the snow load on the ground;
Loads evaluationLoads evaluation on the current floor plan: Permanent loads from the self weight of the slabsType of floorTotal surfaceSurface with warm flooringSurface with cold flooringLoads on warm flooring solutionLoads on cold flooring solutionWeight of the warm flooring solutionWeight of the cold flooring solutionTotal weightNo. of similar floorsTotal of each type of floor
PiStSwScgcgrGwGcG-Gt
-m^2m^2m^2KN/m^2KN/m^2KNKnKn-KN
P118,19018,195,9498,930162,4367162,43672324,8734
P218,6925018,69255,9498,930166,924166,9242333,8481
P318,1718,1705,9498,93108,09330108,09332216,1867
P420,3520,3505,9498,93121,06220121,06221121,0622
P519,702514,84,90255,9498,9388,045243,77933131,82451131,8245
P618,710,717,997,5538,9380,8926371,3507152,24331152,2433
P718,1913,64,595,9498,9380,906440,9887121,89511121,8951
P84,5604,565,9498,93040,720840,7208281,4416
total1483,375
Variable loadsType of floorTotal surfaceUnitary variable loads Variable loadNo.of similar floorsTotal of each type of floors
PiStqQ-Qt
-m^2KN/m^2KN/m^2-KN
123456
P118,192,545,475290,95
P218,69252,546,73125293,4625
P318,171,527,255254,51
P420,351,530,525130,525
P519,70252,549,25625149,25625
P618,7356,1156,1
P718,192,545,475145,475
P84,562,511,4222,8
449,0788
Permanent loads from the self weight of the walls
Permanent loads from the self weight of the ext walls
Type of floorTotal surfaceThe surface of the openingsWalls surface without openingsLoads on wall without openingsLoads from carpentryWeight of the wall without openingsWeight of the carpentryTotal weight of the wallNo.of similar wallsTotal of each type of floors
EiStSoSngpgoGnGoG-Qt
-m^2m^2m^2KN/m^2KN/m^2KNKNKN-KN
E115,962,413,567,7490,5105,07641,2106,27642212,5529
E215,961,9214,047,7490,5108,7960,96109,7562219,5119
E310,922,768,163,49650,528,531441,3829,91144259,82288
E410,082,167,923,49650,527,692281,0828,77228257,54456
E510,920,7210,23,49650,535,66430,3636,0243272,0486
E610,082,47,683,49650,526,853121,228,05312128,05312
E710,081,688,43,49650,529,37060,8430,2106130,2106
E810,083,126,963,49650,524,335641,5625,89564251,79128
731,5358
Permanent loads from the self weight of the int walls
Type of floorTotal surfaceThe surface of the openingsWalls surface without openingsLoads on wall without openingsLoads from carpentryWeight of the wall without openingsWeght of the carpentryTotal weight of the wallNo.of similar wallsTotal of each type of floors
IiStSoSngpgoGnGoG-Qt
-m^2m^2m^2KN/m^2KN/m^2KNKNKN-KN
I115,96015,963,6040,557,51984057,519842115,0397
I215,96015,967,8570,5125,39770125,39771125,3977
I315,962,113,863,6040,549,951441,0551,001442102,0029
I415,962,113,867,8570,5108,8981,05109,9482219,896
I510,081,898,197,8570,564,348830,94565,293832130,5877
I610,921,899,037,8570,570,948710,94571,893712143,7874
I710,08010,087,8570,579,19856079,19856179,19856
I815,962,6613,37,8570,5104,49811,33105,82811105,8281
1021,738
Loads evaluation on the terrace roof plan:
Permanent loads from the self weight of the slab
Variable loadsType of floorTotal surface of the floorUnitary variable loadVariable loadNo. of similar floorsTotal of each type of floors
PterrStqQterr-Qt,terr
-m2KN/m2Kn-KN
1234=2X356=4X5
P1,terr213,541,5320,311320,31
Permanent loads from the self weight of the atticType of floorAttic surfaceLoads from the atticTotal weightNo.of similar wallsTotal load
PiStgcGatt-Gt,att
-m^2KN/m^2KN-KN
E1,att27,364,806131,49221131,4922
Type of floorSurface of the floorLoads on the terrace floorTotal weightNo.of similar floorsTotal loads
PiStgcGterr-Qt
-m^2KN/m^2KN-KN
P1213,549,5722044,00512044,005
Loads evaluation on the whole building
G = G1 + G2 + G3 + G4 + G5 G1 = G2 = G3 = G4 = Gc G=4xGc + G5= 16845,4 KN Gc = Ge,walls + Gi,walls + Gslab + ndi(Qlive or Gd,walls)= 3416,28 KN G5 = Gt,terr + Gt,att + 0.5 Gwall + ndi (Sk or Qk)= 3180,24 KN
Active cross-section of vertical elements (stanchions)
Element no. 1
Iy= 407752.2850 cm4=0.0041 m4;Ix= 111918304.62 cm4= 1.119 m4. Active sections to shear force:Amt= b*h/k= 20*390/1.1= 7090.91 cm2= 0.71 m2.Element no. 2
Moments of inertia:Iy= 152724057.9710 cm4=1.527 m4;Ix= 626666.6667 cm4= 0.0062 m4. Active sections to shear force:Amt= b*h/k= 20*420/ 1.1= 7636.3636 cm2= 0.7636 m2.Element no. 3
Moments of inertia:Iy= 1959557.8365 cm4= 0.0196 m4Ix= 19943960.6821 cm4= 0.1994 m4 Active sections to shear force:Amt= b*h/k= 20*100/ 1.1= 1818.1818 cm2= 0.181 m2
Element no. 4
Moments of inertia: Iy= 42824506.4480 cm4= 0.428 m4;Ix= 802032785.2187 cm4= 8.02 m4. Active sections to shear force:Amt= b*h/k= 20*640/1.1= 11636.36 cm2= 1.163 m2
Element no. 5
Moments of inertia: Iy= 349549.3146 cm4= 0.0035 m4 Ix= 57586056.746 cm4= 0.576 m4 Active sections to shear force:Amt= b*h/k= 20*310/ 1.1= 5636.3636 cm2= 0.5636 m2
Active cross section of the girdes/coupling beamsBeam no. 1
Moments of inertia:Iy= 1675104.1667 cm4= 0.0167 m4Ix= 475416.6667 cm4= 0.00475 m4 Active area :Amt= b*h/k= 1545.4545 cm2= 0.1545 m2
Beam no. 2
Moments of inertia:Iy= 1023681.3946 cm4= 0.0102 m4Ix= 9013971.7916 cm4= 0.0901 m4 Active area:Amt= b*h/k= 20*175/1.1= 3181.818 cm2=0.3181 m2
Beam no.3
Moments of inertia:Iy= 654811.2108cm4= 0.00654 m4Ix= 8997592.2445cm4= 0.0899 m4 Active area:Amt= b*h/k= 20*175/1.1= 3181.818 cm2= 0.3181 m2
Seismic load distribution Corner period Tc for Brasov is: 0.7 s. Base shear force : Fb= 0.18*Gtot= 0.18*16845.4=3032.172 KN Gtot= Gterrace+4*Gfloor= 16845.4 KN Coefficient s for 5 storeys is 10.87.
Shear walls with two lines of openingsThe wall consists of stanchion elements E1, E3, E5, and coupling beams R3 and R2. The structure is symmetrical so that there are two walls like that.
m4
Em= 3000 KN/cm2= 3*107KN/m he= 2.80 m.
L= 827.81 cm= 8.27 m l2=l0+2a=200+2*29.75= 259.5 cm= 2.59 m
l3=160+2*29.75= 219.5 cm=2.19 m
s=0.142the overall moment of inertia:
+0.71= 1.4546 m2
Shear walls with one unsymmetrical opening The wall consists of the coupling beam R1 and of the stanchions E2 and E4.The structure is symmetrical so that there are two walls like that.
L= 5.897 ml=1+2*a=1+2*0.35*0.85=1.595 m
1.
2.
s= 0.426 the overall moment of inertia:
Distribution factor computation:
Shear base seismic force:
The equivalent load distributed along the height of the storey :
Determination of the N,V,M diagrams for the wall no. 2, wall with one line of unsymmetrical openings.The moments in the stanchions are computed with the relation:
Shear force and bending moment in the stanchions:SectionmsMmeMm2Mm4Vm2Vm4
0-114,13313,872,5598663311,310,371102480,0385
1-0-8,07-1896,66-1,46511-1895,2
1-29,12138,7391,6521122137,0870,344639445,8069
2-1-3,5-822,592-0,63543-821,956
2-35,091196,2840,9240931195,3590,295405382,1202
3-2-0,29-68,1576-0,05265-68,105
3-42,09491,20480,379441490,82540,221553286,5901
4-31,51354,88960,274142354,6155
4-50,2968,157610,0526568,104960,123085159,2167
5-41,71401,89490,310452401,5844
Shear force and bending moments in the coupling beams:
SectionmsMmeMm2Mm4Mr4Mr2Vr
0-114,13313,872,5598663311,31-1416,11-1,09475-1417,21
1-0-8,07-1896,66-1,46511-1895,2
1-29,12138,7391,6521122137,087-1315,13-1,01668-1316,15
2-1-3,5-822,592-0,63543-821,956
2-35,091196,2840,9240931195,359-1127,25-0,87144-1128,13
3-2-0,29-68,1576-0,05265-68,105
3-42,09491,20480,379441490,8254-845,441-0,65358-846,094
4-31,51354,88960,274142354,6155
4-50,2968,157610,0526568,10496-469,689-0,3631-470,052
5-41,71401,89490,310452401,5844
Gravitational load distribution
Axial load and shear force o the shear wall:SectionAxial load on the shear wall [N]M2 stanchionM4 stanchion
Axial loadShear force VTotal axial load on the stanchionAxial loadShear force VTotal axial load on the stanchion
0-12245455,7-1417,20,3712244038,5-1417,2480,08352242621,297
1-02021076,992021076,992021076,992
1-21765881,63-1316,140,3441764565,49-1316,14445,80691763249,352
2-11541504,641541504,641541504,636
2-31286309,28-1128,130,2951285181,15-1128,13382,12021284053,026
3-21061932,281061932,281061932,279
3-4806736,919-846,090,221805890,829-846,09286,5901805044,7394
4-3582359,923582359,923582359,9231
4-5327164,563-470,050,123326694,513-470,05159,2167326224,4631
5-4000