Trabajo i Phase 3

Analysis of concrete strengths and allowable stresses

2800 (f'ci) psi 0.35 8000 (f'c) psi

-317 psi 6 -536.656

1260 psi 0.45 3600Allowable compression

At release In service

Concrete strength

Allowable tension

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 5 10 15 20 25

Co

mp

ress

ive

Stre

ngt

h (

psi

)

Age (days)

Plank Concrete Strength vs. Age in days

4000 (f'c) psi

6 -506 8

0.45 1800 0.45

Age fc

0.1 280

1 2800

28 8000

In service Topping concrete

30

Explanation: I have chosen concrete strength and subsequent allowable compression and tension, staying within the ranges required. Also, I have plotted the evolution in time of concrete strength.

Design of cross section and section properties

tt= 2 in

y tp= 8 in

48

5.5

2

6.1

Actual number of voids per plank 6

Center of voids from bottom (in.) 4.25

1.5

1

Section Properties without Topping

Area y bar (A)(ybar) Ig d Ad2

Topping 0 0 0 0 0 0

Plank 384 4 1536 2048 -0.1476 8.365444

Voids -143 4.25 -606 -269.508 -0.3976 -22.5348

Totals 241 930 1778 -14.1694

241 in2

3.85 in2

1764 in2

3.85 in2

4.15 in2

458 in2

425 in2

c to bottom

c to top

S (bottom of plank)

Y Bar (from bottom)

S (top of plank)

Moment of inertia

width

Plank Width-inches

Void Diameter-inches

Min spacing between voids (in.)

Calc number of voids per plank

Clear depth below voids (in.)

Clear depth above voids (in.)

Area

Explanation: I have chosen all dimensions of plank, topping and voids, and below I have made all the calculations for the resulting section properties, with and without topping


Area y bar (A)(ybar) Ig d

Topping 96 9 864 32 3.68

Plank 384 4 1536 2048 1.32

Voids -143 4.25 -606 -269.508 1.07

Totals 337 1794 1810

337 in2

5.32 in2

3616 in2

5.32 in2

2.68 in2

4.68 in2

680 in2

1348 in2

772 in2S (top of topping)

c to bottom

c to top of plank

c to top of topping

Area

Y Bar (from bottom)

S (bottom of plank)

S (top of plank)

Moment of inertia

Explanation: I have chosen all dimensions of plank, topping and voids, and below I have made all the calculations for the resulting section properties, with and

Ad2

1302

666

-162

1806

Prestressing Configuration and Forces

Wire Dia Wire Dia

3/8. 0.375

7/16. 0.438

1/2. 0.500

9/16. 0.563

0.6 0.600

9

0.375 in

0.085 in2

1 inches

1.19 inches

-2.66 inches

270 KSI

0.75

0.6

17.2 Kips

155 Kips

642 psi

413 in-Kips

-970 psi

-329 psi

901 psi

1543 psi

Flexural prestressing tension on top

Initial prestressing net tension on top Service prestressing net tension on top

Service force per strand

Initial precompression force Service precompression force

Flexural prestressing compression on bottom Flexural prestressing compression on bottom

Initial prestressing compression on bottom Service prestressing compression on bottom

Initial untopped prestressing moment Service untopped prestressing moment


Initial precompression axial stress Service precompression axial stress

Center of strand from bottom

Untopped eccentricity of prestressing force

Ultimate strength

Initial stressing percentage

Service load stressing percentage

Initial stressing at release of strands At Service after losses

Initial force per strand

Bottom cover on strand

270 KSI wire strand

Number of prestressing strands

Nominal size of prestressing strands

Diameter of prestressing strands

Area of strand

Area

0.085

0.115

0.153

0.192

0.215

13.8 Kips

124 Kips

513 psi

330 in-Kips

-776 psi

-263 psi

721 psi

1234 psi


Service prestressing net tension on top


Service precompression force

Flexural prestressing compression on bottom

Service prestressing compression on bottom

Service untopped prestressing moment

Service precompression axial stress

At Service after losses

270 KSI wire strand

Explanation: I have chosen number and size (from the table above) of the prestressing strands. Also, I have decided the situation of those strands in the cross section and their strength and relaxation with time. Finally, I have made all the calculations for forces, moments and stresses in the plank, initially and after losses.

Analysis of load history, concrete strength, and allowable superimposed load

Span 28 feet

100 psf

15 psf

115 psf

23005 ft-lb

9147 ft-lb

Plank area 241 in2 Topped Sb 680 in3

Untopped Sb 458 in3 Topped St plank 1348 in3

Untopped St 425 in3 Topped St topping 772 in3

Superimposed load on topped plank (psf) 295 847

1800 2956

Final stress state with full superimposed load 701 1045

Superimposed load moment (ft lb) 115833 332027

Tolerable stress from additional LL

3600

Topped plank, no external load 0 644

Plank at service before topping applied, psi 0 386

Self weight topping flexure 0 258

Max allowable stress 1800

Service Prestressing flexure, psi 0 -776

Self Weight Plank, psi 0 649

Service Prestressing Compression, psi 0 513


Plank at release of strands, psi 0 320

Initial prestressing flexure, psi 0 -970

Plank self weight moment

Maximum allowable superimposed load=

Initial prestressing compression, psi 0 642

Topping self weight moment

Top of topping Top of plank

Superimposed Live Load=

Superimposed Dead Load=

Analysis of load history, concrete strength, and allowable superimposed load 140 lb/ft3

140 lb/ft3

58.7 psf

23.3 psf

82.0 psf

TRUE TRUE

134

-929

-403 TRUE

52636

-537

392 NA

632 NA TRUE TRUE

-240

TRUE TRUE

721

-603

513

TRUE

-603 Topping is OK Top of plank is OK

940 NA TRUE

901

Bottom of plank OK

Topping weight

642

Topped plank weight

Bottom of plank

Plank concrete density

Topping density

Untopped plank weight

Explanation: 1) I have chosen span length. 2) With the values of density above, I've calculated self weights and the subsequent produced moments. 3) With the values of self weights, prestressing stresses, and a superimposed load of 180 psf, I've calculated all the stress states throughout the whole process, since fabrication to service. 4) Finally, I have compared if these stress states are acceptable, since the point of view of allowable stresses calculated in the next sheet.

Design of cross section and section properties

tt= 2 in

y tp= 5 in

48

3

2

9.2

Actual number of voids per plank 9

Center of voids from bottom (in.) 2.5

1

1


Area y bar (A)(ybar) Ig d Ad2

Topping 0 0 0 0 0 0

Plank 240 2.5 600 500 0 0

Voids -64 2.5 -159 -35.7847 0 0

Totals 176 441 464 0

176 in2

2.50 in2

464 in2

2.50 in2

2.50 in2

186 in2

186 in2

c to bottom

c to top

S (bottom of plank)

Y Bar (from bottom)

S (top of plank)

Moment of inertia

width

Plank Width-inches

Void Diameter-inches

Min spacing between voids (in.)

Calc number of voids per plank

Clear depth below voids (in.)

Clear depth above voids (in.)

Area

Explanation: I have chosen all dimensions of plank, topping and voids, and below I have made all the calculations for the resulting section properties, with and without topping


Area y bar (A)(ybar) Ig d

Topping 96 6 576 32 2.27

Plank 240 2.5 600 500 1.23

Voids -64 2.5 -159 -35.7847 1.23

Totals 272 1017 496

272 in2

3.73 in2

1258 in2

3.73 in2

1.27 in2

3.27 in2

337 in2

993 in2

385 in2S (top of topping)

c to bottom

c to top of plank

c to top of topping

Area

Y Bar (from bottom)

S (bottom of plank)

S (top of plank)

Moment of inertia

Explanation: I have chosen all dimensions of plank, topping and voids, and below I have made all the calculations for the resulting section properties, with and

Ad2

493

365

-97

762

Prestressing Configuration and Forces

Wire Dia Wire Dia

3/8. 0.375

7/16. 0.438

1/2. 0.500

9/16. 0.563

0.6 0.600

8

0.438 in

0.115 in2

1.08 inches

1.30 inches

-1.20 inches

270 KSI

0.75

0.6

23.3 Kips

186 Kips

1056 psi

224 in-Kips

-1205 psi

-149 psi

1205 psi

2261 psi


Initial prestressing net tension on top Service prestressing net tension on top


Initial precompression force Service precompression force

Flexural prestressing compression on bottom Flexural prestressing compression on bottom

Initial prestressing compression on bottom Service prestressing compression on bottom

Initial untopped prestressing moment Service untopped prestressing moment


Initial precompression axial stress Service precompression axial stress

Center of strand from bottom

Untopped eccentricity of prestressing force

Ultimate strength

Initial stressing percentage

Service load stressing percentage

Initial stressing at release of strands At Service after losses

Initial force per strand

Bottom cover on strand

270 KSI wire strand

Number of prestressing strands

Nominal size of prestressing strands

Diameter of prestressing strands

Area of strand

Area

0.085

0.115

0.153

0.192

0.215

18.6 Kips

149 Kips

845 psi

179 in-Kips

-964 psi

-119 psi

964 psi

1809 psi


Service prestressing net tension on top


Service precompression force

Flexural prestressing compression on bottom

Service prestressing compression on bottom

Service untopped prestressing moment

Service precompression axial stress

At Service after losses

270 KSI wire strand

Explanation: I have chosen number and size (from the table above) of the prestressing strands. Also, I have decided the situation of those strands in the cross section and their strength and relaxation with time. Finally, I have made all the calculations for forces, moments and stresses in the plank, initially and after losses.

Analysis of load history, concrete strength, and allowable superimposed load

Span 28 feet

28.4 psf

15 psf

43.4 psf

16805 ft-lb

9147 ft-lb

Plank area 176 in2 Topped Sb 337 in3

Untopped Sb 186 in3 Topped St plank 993 in3

Untopped St 186 in3 Topped St topping 385 in3

Superimposed load on topped plank (psf) 147 431

1800 2042

Final stress state with full superimposed load 530 1763

Superimposed load moment (ft lb) 57757 168984

Tolerable stress from additional LL

3600

Topped plank, no external load 0 1558

Plank at service before topping applied, psi 0 967

Self weight topping flexure 0 591

Max allowable stress 1800

Service Prestressing flexure, psi 0 -964


Service Prestressing Compression, psi 0 845


Plank at release of strands, psi 0 937

Initial prestressing flexure, psi 0 -1205

Plank self weight moment

Maximum allowable superimposed load=

Initial prestressing compression, psi 0 1056

Topping self weight moment

Top of topping Top of plank

Superimposed Snow Load=

Superimposed Dead Load=

Analysis of load history, concrete strength, and allowable superimposed load 140 lb/ft3

140 lb/ft3

42.9 psf

23.3 psf

66.2 psf

TRUE TRUE

48

-668

-474 TRUE

18766

-537

132 NA

723 NA TRUE TRUE

-591

TRUE TRUE

964

-1086

845

TRUE

-1086 Topping is OK Top of plank is OK

1175 NA TRUE

1205

Bottom of plank OK

Topping weight

1056

Topped plank weight

Bottom of plank

Plank concrete density

Topping density

Untopped plank weight

Explanation: 1) I have chosen span length. 2) With the values of density above, I've calculated self weights and the subsequent produced moments. 3) With the values of self weights, prestressing stresses, and a superimposed load of 180 psf, I've calculated all the stress states throughout the whole process, since fabrication to service. 4) Finally, I have compared if these stress states are acceptable, since the point of view of allowable stresses calculated in the next sheet.

Wall geometry

Concrete Masonry Unit Geometry

Concrete Masonry Unit Properties

Mortar properties

Masonry properties

f’m

Mortar bedding

Grouted

Modulus of Elasticity

Masonry Design Choices

Width of wall 12 in

Horizontal Length 84 ft

Height (floor to floor height is usually also the maximum unbraced length) 10.5 ft

Center-to-center spacing (= span of precast plank) 28 ft

Width of unit (Nominal 4, 6, 8, 10, 12-inch) 12 in

Concrete Unit strength (1900 to 6000 psi) 3050 psi

Concrete Unit density (80 to 140 lb/ft3) 120 lb/ft3

Type: M, S, N, O N

As determined as a function of concrete unit strength and mortar type 2000 psi

Face Shell, Full Bedding Full

Ungrouted, partially grouted, fully grouted Ungrouted

Function of unit strength and mortar type 2315000 psi

Masonry Design Choices

Area 57.8 in2

Moment of Inertia 1065 in4

Section Modulus 183 in3

Radius of Gyration 4.29 in

Weight (ungrouted) 55.5 psf

Masonry Section Properties (per ft of wall)

82.0 psf

15 psf

100 psf

197.0 psf

28 ft

2296.5 lb

420 lb

2800 lb

5516.5 lb

Floor plank self weight

DL

LL

Floor loads per foot of wall

Pressures

Floor plank self weight

DL

LL

Floor Length

Forces

66.2 psf

15 psf

0 psf

28.4 psf

110 psf

28 ft

1854 lb

420 lb

0 lb

793.8 lb

3068 lb

Snow

Roof length

Roof plank self weight

DL

LL

Snow

Roof loads per foot of wall

Pressure Loads

Forces

Roof plank self weight

DL

LL

DL and Self weight 2274 lb

DL and Self weight+LL+Snow 3068 lb

Self weight 55.5 psf

Height 10.5 ft

Self weight 582.75 lb

Pressures

Force

Wall loads per foot of wall

Calculation of the Snow Load

According to New York State Building Code, we have to follow the method described by ASCE 7, Section 7.3

Step 1: We identify the ground snow load in the area of Ithaca using the figure below.

According to the figure above, we find that the ground snow load is 45.

Step 2: Determine the flat roof snow load using the ground snow load.

Determining Exposure Factor

According to terrain categories listed in ASCE Section 1609.4, the building site fits into category B. Therefore, Exposure factor is:

Step 3: Determing Thermal Factor

We choose the value, 1.0 for Thermal Factor. The structure doesn't seem to fit any of the bottom 3 categories.

Step 4: Snow Importance Factor

We determine that the Snow Importance Factor is 1.

Step 5: Calculate the flat roof snow load:

Pf=

According to terrain categories listed in ASCE Section 1609.4, the building site fits into category B. Therefore, Exposure factor is: 0.9

28.4 psf

30 psf

24 psf

15 psf

basic wind

wind pressure (k=0.8)

wind suction (k=0.5)

Wind loads

Calculations per foot of wall

21948 lb

380 psi

4.29 in

29.4

478.0 psi Code requirements

0.79

325311 lb

TRUE

TRUE

Bearing walls- Interior-Pure compression

Axial Load(DL+LL)

fa

r

h/r

Fa

fa/Fa

Peuler

ALL THE CALCULATIONS IN THE TABLE BELOW ARE PER FEET OF WALL

Load CaseDL and Self

Weight

DL and Self

weight + LL +

Snow

DL and Self

weight + LL +

Snow + Wind

pressure

DL and Self

weight + LL +

Snow + Wind

suction

Axial compression

stress at mid-height

of exterior wall, f a

30 37 37 37

Computed value of

F a(Increase by 1/3 when

wind is present)

478 478 637 637

Max value of P 1720 2117 2117 2117

Computed value of

1/4P e(Increase by 1/3

when wind is present)

81328 81328 108437 108437

Max value of P

acceptable?TRUE TRUE TRUE TRUE

Flexural

compression stress

at mid-height, f be

due to plank eccentricity

28 35 35 35

Flexural

compression stress

at mid-height, f bwp,

due to wind pressure

0 0 -22 0

Flexural

compression stress

at mid-height, f bws

due to wind suction

0 0 0 14

Worst case Net

flexural

compression stress

at mid-height, fb

compr.

28 35 13 48

Bearing walls- Highest exterior wall -combined axial and bending stresses

Computed value of

F b(Increase by 1/3 when

wind is present)

667 667 889 889

Flexural tension

stress at mid-

height, f be

28 35 35 35

Flexural tension

stress at mid-

height, f bwp

0 0 -22 0

Flexural tension

stress at mid-

height, f bws

0 0 0 14

Worst case Net

flexural tension

stress at mid-

height, fb tension

28 35 13 48

Worst case NET

flexural tension

stress at mid-height

=(fa-fb)

2 2 24 -12

Allowable tension

stress (Increase by 1/3

when wind is present)

19 19 25 25

Tension stress


Value of fa/Fa +

fb/Fb

0.10 0.13 0.07 0.11

Is this value


DL and Self

weight + Wind

pressure

DL and Self

weight + Wind

suction

30 30 psi

637 637 psi

1720 1720 lb

108437 108437 lb

TRUE TRUE

28 28 psi

-22 0 psi

0 14 psi

7 42 psi

Bearing walls- Highest exterior wall -combined axial and bending stresses

fa = P/A = actual axial compression stress on wall or strip of

wall.

Fa = allowable masonry compression stress as given by

Code Equations (2-12) and (2-13)

P = actual axial force on wall or strip of wall

Pe = Modified Euler bucking load for wall or strip of wall. See code

eqn (2-11)

Is P (1/4) Pe?

fbe = Mbe/S, where Mbe is due to eccentricity of load.

fbwp = Mbwp/S, where Mbwp is due to wind pressure. For our

project in the exterior walls the wind pressure moment is

opposite in sign to the eccentricity moment.

fbws = Mbws/S, where Mbws is due to wind suction. For our

project in the exterior walls the wind suction moment is of the

889 889 psi

28 28 psi

-22 0 psi

0 14 psi

7 42 psi

23 -12 psi

25 25 psi

TRUE TRUE

0.05 0.09

TRUE TRUE

Fb = allowable masonry flexural compression stress as

given by Code Equation (2-14).

fbe = Mbe/S, where Mbe is due to eccentricity of load.

fbwp = Mbwp/S, where Mbwp is due to wind pressure. For our



fbws = Mbws/S, where Mbws is due to wind suction. For our


same sign as the eccentricity moment.

fb tension = the greater of

[Mbe/S - Mbwp/S] or

[Mbe/S+ Mbws/S]

Net tension stress= Axial compression stress

[Mbe/S - Mbwp/S] or [Mbe/S+ Mbws/S]

This comes directly from Code allowable tension Table 2.2.3.2.

This is the only permissible way to combine compressive stress in masonry

that originates in axial load with compressive stress in masonry that

Is actual stress allowable stress?

Is the interaction equation satisfied?

= actual axial compression stress on wall or strip of

compression stress as given by

actual axial force on wall or strip of wall

Modified Euler bucking load for wall or strip of wall. See code

is due to eccentricity of load.

is due to wind pressure. For our



is due to wind suction. For our


allowable masonry flexural compression stress as

is due to eccentricity of load.

is due to wind pressure. For our



is due to wind suction. For our


stress= Axial compression stress fa , minus the greater of

This comes directly from Code allowable tension Table

This is the only permissible way to combine compressive stress in masonry

that originates in axial load with compressive stress in masonry that

Load CaseDL and Self

Weight

DL and Self

weight + LL +

Snow

DL and Self

weight + LL +

Snow + Wind

pressure

Axial compression stress at

mid-height of exterior wall,

f a

50 152 153

Computed value of F a

(Increased by 1/3 when wind is present)

Computed value of 1/4P e

(Increased by 1/3 when wind is present)

Max value of P acceptable? TRUE TRUE TRUE

Flexural compression stress

at mid-height, f be due to plank

eccentricity

6 39 39


at mid-height, f bwp, due to wind

pressure

0 0 -22


at mid-height, f bws due to wind

suction

0 0 0

Worst Case Net combined

flexural compression stress

at mid-height, f b compr.

6 39 60

Computed value of F b

(Increase by 1/3 when wind is present)

Flexural tension stress at mid-

height, f be

6 39 39

Worst case combined

6

Bearing walls- Lowest exterior wall -combined axial and bending stresses

0 -22

39 17


height, f bws

0 0 0


height, f bwp

0

383177

510902

500 500 667

Max value of P 2885 8799 8820

478

637

flexural tension stress at mid-

height, f b tension

Worst case NET flexural

tension stress at mid-height =

f a - f b tension

Allowable tension stress (Increase by 1/3 when wind is present)

19 19 25

Tension stress acceptable? TRUE TRUE TRUE

Is this value acceptable? TRUE TRUE TRUE

44 114 136

6

Value of fa/Fa + fb/Fb 0.12 0.40 0.34

39 17

DL and Self

weight + LL +

Snow + Wind

suction

DL and Self

weight +

Wind

pressure

DL and Self

weight +

Wind suction

152 50 50 psi

psi

psi

lb

lb

lb

lb

TRUE TRUE TRUE

39 6 6 psi

0 -22 0 psi

14 0 14 psi

52 28 20 psi

psi

psi

39 6 6 psi

psi

psi

psi

psi

psi

20-15

-22

Bearing walls- Lowest exterior wall -combined axial and bending stresses

0

52

0

14 0 14

383177

510902

667 667 667

8812

478

637

28992907

psi

psi

psi

25 25 25 psi

TRUE TRUE TRUE

TRUE TRUE TRUE

20

100 66 30

-15

0.08 0.130.40

52

LATERAL LOAD ANALYSIS

Floor

1st floor 3909 kips 0 ft

2nd floor 11852 kips 10.8 ft Base Shear 2170

3rd floor 11852 kips 22.0 ft ∑(wi*hi) 500996

Roof 3385 kips 33.0 ft

total 30998

Distance between floors 11.2 ft

Distance between last floor and roof 11.0 ft

FORCES PRODUCED BY EAST-WEST WIND

Floor pressure + suction (psf) associated area(ft2) Force(kips)

2nd floor 39 952 37.1

3rd floor 39 952 37.1 resultant base wind force

Roof 39 490 19.1

(taking into account plank thickness)

FORCES PRODUCED BY NORTH-WEST WIND

Floor pressure + suction (psf) associated area(ft2) Force(kips)

2nd floor 39 1288 50.2

3rd floor 39 1288 50.2 resultant base wind force

Roof 39 663 25.9

(taking into account plank thickness)

Effective Seismic Weight Height

Base shear 2170 kips

kips 2nd floor 556 kips

kips-ft 3rd floor 1129 kips

Roof 484 kips

resultant base wind force 93.4 kips

resultant base wind force 126 kips

Earthquake forces

PROPERTIES OF SHEAR WALLS:Number of shear walls : 2

Wall geometry Thickness of wall 4 in

Horizontal Length 6 ft

CMU Geometry Width of unit (Nominal 4, 6, 8, 10, 12-inch) 4 in

CMU Properties

Concrete Unit strength (1900 to 6000 psi) 2150 psi

Concrete Unit density (80 to 140 lb/ft3) 120 lb/ft3

Mortar properties Type: M, S, N, O N

Masonry properties

f’m

As determined as a function of concrete unit strength and mortar type1500 psi

Mortar bedding Face Shell, Full Bedding Full

Grouted Ungrouted, partially grouted, fully grouted Grouted Same density as cmu

Modulus of Elasticity Function of unit strength and mortar type 1920000 psi

Area 261 in2

Moment of Inertia 112908 in4

Section Modulus 3136 in3

Radius of gyration 21 in

Weight (grouted) 76 psf

SHEAR WALLS- Wind or EQ force in East-West Direction

Masonry Section Properties (per foot of height)

ANALYSIS OF FORCES AND STRESSES

Forces over each shear wall

EQ (lb) Wind (lb)

1st floor 1085 47

2nd floor 278 19

3rd floor 565 19

Roof 242 10

Moments at base of each shear wall

EQ 23438 lb-ft

Wind 925 lb-ft

Shear force at base of each shear wall (assumption rectangular cross section)

EQ 6.2 psi

Wind 0.3 psi

Slf weight of shear wall

Total 15222 lb

Stress 58.3 psi

Flexural tension at base

EQ 89.7 psi

Wind 3.54 psi

Net tension at base

EQ 31.4 psi

Wind -54.8 psi

Allowable tension 63 psi

Tension is OK

EQ TRUE

Wind TRUE

Axial compression and flexure:

fa 58 psi fb

r 21 in Fb

h 399 in fb/Fb

h/r 19.2

Fa 491 psi

fa/Fa 0.12

P 15222 lb

Peuler 1.34E+07 lb

EQ Wind

Compression is OK TRUE TRUE

Buckling is OK

Shear analysis:

EQ Wind

Shear stress 6.2 0.27 psi

Allowable shear stress

a) psi

b) psi

c)running bond, grouted psi

Shear is OK

86.2

TRUE

TRUE

58

120

Same density as cmu

SHEAR WALLS- Wind or EQ force in East-West Direction

EQ Wind

89.7 3.54 psi

psi

0.13 0.01

667

Documents

Trabajo i Phase 3