Beam & Colum Design - CE 161

7/27/2019 Beam & Colum Design - CE 161

1/198

Material Property: Model: Tributary Area (refer to analysis)

fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90

u = 0.003

Cover= 70.00 mm

Assume Section : l= 1.90 m

b = 230 mm

d= 340

h = 410 mm

slab thcikness 160 mmService Loads:

Dead loads: KN/m3

KN/m2

KN/m

Weight of beam (Wb) 25.00 ---- 2.36Weight of Slab (Ws) 25.00 ---- 7.6

Parapet (Normal weight concrete,Wp1) 21.20 ---- 1.91

Parapet (Decorative Tile Finished, Wp2) ---- 0.77 0.77

Live Loads: Kpa KN/m

2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.83

Wu(slab)= 1.2DL + 1.6LL = 16.42

Wu(Parapet)= 1.2DL= 3.21

Wu= 22.46

Beam RB-1:

Line of symmetry

Note: Choose biggest value of Shear & Moment.

Shear Diagram:

Two-Story office Building Date Prepared:

A. Design of Beams Checked By:

Beam RB-1 - Roof Deck Framing Plan Rating:

Wb=

Wu

Ws=

L = 7.60 m L = 7.60 m

Wu = +

Wp2=

Wp1=(

l


2/198

Design For Flexure:

Design Moment:

Mu= 26 KN-m

Designer's Preferred Steel Ratio:

b = 0.0421753

(desired) = 0.0253052

Cross Section of Beam: Nominal Moment:

Mn = 28.89 Kn-m

bd2

= 5018688.488 mm3

b = 250 mm Fexural Resistance factor

d = 141.69 mm

h' = 141.69 mm R= 5.75626h (assume) > h', ok!

Final:

b = 250 mm

d = 330 mm

h = 400 mm

Area of Steel:

Roots:

a = 46793235022 1 = 0.14046

b = -6757789500 2 = 0.00396

c = 26000000 new = 0.00396 choose the smaller

rho new < rho min, use rho min

As= 418.78 mm

2Final: = 16 mm

Bar Diam.()= 16 mm n= 3 bars

no. of bars (n)= 2.08 bars As= 603.187 mm2

Checking for ACI requirements:

Steel ratio:

max = 0.03163

actual = 0.00731

min = 0.00508 0.00439 0.00508

rho actual > rho min, ok!

rho max> rho actual, ok!

Depth of Rectangular Stress Block (a): Check if Tension Steel Yields:

a = 33.31345 mm Strain of steel Yeilds:

Choose the biggest Mu for

beam dept(d)


beam depth (d)

bd2=Mu/R Mn = Mu/

a^2+b+c=0

a = (As

n =

As/(((2)

= - ^ -

Mu = Mn= fybd^2 (1-0.59 fy/(f^ c))


3/198

Design Moment:

(+)Mu= 15 KN-m

Cross Section of Beam:

b = 250 mm

d = 330 mm

h = 400 mm

Area of Steel:

Roots:

a = 46793235022 1 = 0.14216

b = -6757789500 2 = 0.00225



As= 418.78 mm

2Final: = 16 mm

Bar Diam.()= 16 mm n= 3 bars

no. of bars (n)= 2.08 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00731

min = 0.00508 0.00439 0.00508


rho max > rho actual, ok!

Check if Stirrups are needed:

Ultimate Shear (Vu)= 40.00 KN/m

Shear Strenght by Concrete (Vc) = 67.99 KN/m

Vc= 50.99 KN/m

Vu < 0.5Vc, Stirrups not needed!

Vu < Vc, Provide minimum shear reinforcement!

Design for Shear Reinforcement:

= 8 mm

Av min.= 100.5312 mm2

Maximum Spacing (smax):

a.) smax1= 165 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 165 mm

Positive Moment

a^2+b+c=0= - ^ -

Mu = Mn= fybd^2 (1-0.59 fy/(f^ c))

Av(min) =


4/198

Bar cut-off and Development Length:

Moment Diagram:

Theoritical Bar Cut-off Graph: Wight & macGregor "Reinforced Concrete",6th edition, pp.1102

Bar Cut-off (1/3 and 2/3 of bars that satisfy the ACI code)

As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m

Moment x (1/3)As (2/3)As %As (cut-off) Factor Cut-off Positive 1 201.06 66.67 0.260 0.88

---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35

* Refer to Theoritical Bar Cut-Off Graph

Bar Spacing (s): clear spacing between parallel bars

s= 23 mm

s < 2db, use other cases equation for ld

Factors (ACI CODE 2010):

t= 1

e= 1

s= 1

= 1

Developement Length:

ld= 0.44 m

12db= 0.19 m

d= 0.33 m

ld=12fyte/(25(fc)) db

As%= (As -As1)/As x 100

Cut-Off= factor x 100

s =(b-2(cover+stirrup)-


5/198


6/198

Total 7288*Verify actual to minimize cost


7/198


8/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm

Assume Section : l1= 1.90 m

b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m



2.4 9.12

Ultimate Load: KN/mWu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 28.27

Wu= 30.43

Beam RB-2:

Line of symmetry


Shear Diagram:




Wb=

l1

Wu

Ws=

L = 7.60 m L = 7.60 m

Ws + Wp

Wu=Wb +

1

)

l2


9/198

Design For Flexure:

Design Moment:

Mu= 165 KN-m


b = 0.0421753

(desired) = 0.0253052


Mn = 183.33 Kn-m

bd2

= 31849369.25 mm3


d = 356.93 mm

h' = 356.93 mm R= 5.75626h' > h(assume), Revise Section!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.11571

b = -7173558000 2 = 0.02871


rho new > rho min, use rho new

As= 2440.16 mm

2Final: = 20 mm

()= 20 mm n= 8 bars

(n)= 7.77 bars As= 2513.280 mm2


Steel ratio:

max = 0.03163

actual = 0.02957

(governs) min = 0.00508 0.00439 0.00508






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

n =

= 0.851

(^)/

(600/(600+))

=

(10.59/(

^))

=((^24))/2

Mu = = ^2(10.59/(^))


10/198

Design Moment:

(+)Mu= 84 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.13156

b = -7173558000 2 = 0.01285



As= 1092.56 mm

2Final: = 20 mm

()= 20 mm n= 4 bars

(n)= 3.48 bars As= 1256.640 mm2


Steel ratio:

max = 0.03163

actual = 0.01478

(governs) min = 0.00508 0.00439 0.00508






Vc= 52.54 KN/m

Vu > 0.5Vc, Stirrups are needed!

Vu > Vc, calculate Shear Strenght of steel!

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))


11/198

Design For Shear: Shear Diagram:

At Right Support:

= 8 mm

= 0.75 ACI CODE 2010

Factored Shear Force:

Vu= 123.10 KN

Shear Strength in Concrete:

Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN

Spacing (s) Required:

Av= 100.5312 mm2

S= 100.20 mm

say: 100 mm

Shear Strenght in Steel:

Vs= 70.70 KN

Point of Minimum Stirrups starts:

By ratio and proportion:

Xu= 4.04 m

X1 = 2.32 m

Point where Stirrups are not needed:By ratio and proportion:

Xu= 4.04 m

X2 = 3.18 m

Design For Shear Reinforcement:

Vs

70.70 271954.84 ok, proceed to smax


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Check for maximun spacing:

Vs

Vs

70.70 135.98

smax will not be halved!

Smax = 170 mm

/=/(1)

/=(0.5)/(2)

0.66(^)bwd

Vs = ()/

0.33(^)bwd

s = (

)/()

, smax /224"

0.33(^)bwd

, smax /424"


12/198


At Left Support:

Right = 8 mm

8mm = 0.75 ACI CODE 2010

Factored Shear Force:Vu= 108.20 KN

SAME


Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 127.02 mmsay: 125 mm


Vs= 56.56 KN



Xu= 3.56 m

X1 = 1.83 m

Point where Stirrups are not needed:


Xu= 3.56 m

X2 = 2.70 m


Vs


Maximum Spacing (smax):a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

56.56 135.98


/=/(1)

/=(0.5)/(2)

0.66(^)bwd

Vs = ()/

0.33(^)bwd

s = (

)/()

, smax /224"

0.33(^)bwd

, smax /424"


13/198

15 @ 0.125 m

Rest @ 0.170 m


Moment Diagram:



As= 1256.64 mm2

positive moment

As= 2513.28 mm2

negative moment

ln= 7.20 m

Moment x (1/3)As (2/3)As %As (cut-off) Factor Cut-off

Positive 1 418.88 66.67 0.260 1.87

---- ---- ---- ---- ---- ---- ----

Negative 2 837.76 66.67 0.102 0.73



s= 34 mm



t= 1

e= 1

s= 1


As%= (As -As1)/As x 100



14/198

Beam Details:

Beam Sections Stirrups

Left Midspan Right Left

8mm

*Closed Stirrups were used for the ease of construction*

*Safe & Aesthetic design acquires if beams are uniformly tied (Structral Integrity)

Section:

Estimate for Beam:

Total Volume of Concrete: Class A Mixture: Factor

Vol.conc.= 0.720 m2

Cement (40kg) 9.00

sand 0.50

Use Class A Mixture (1:2:4) Gravel 1.00

No. of Bags of Cement:

No.bags= 6.48 bags

say: 7

Volume of Sand:

Vsand= 0.36 m

3

say: 1

Volume of Gravel:

Vgravel= 0.72 m3

say: 1

Reinforcing Bars:

Top bars: 7 bars (20mm)

Bot. bars: 5 bars (20mm) Direct Counting Method

Stirrups: 10 bars (8mm)

Summary: 2 RB-2

Item Quantity Unit Cost Total

1 @ 0.065 m15 @ 0.125 m

Rest @ 0.170 mO.C

1 @23 @

RestO.C

Vol =L x W x H

No. bags =Volume x Factor

Vol=Vsand x Factor

Vol=Vgravel x Factor


15/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90 l

u = 0.003

Cover= 60.00 mm


b = 250 mm

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m





2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 14.14


Wu= 19.51

Beam RB-3:

Shear Diagram:




(1+2)

s

Wb=

Wu

Ws=

L = 3.80 m

Wu = +

Wp2=

Wp1=(


16/198

Design For Flexure:

Design Moment:

Mu= 56 KN-m


b = 0.0421753

(desired) = 0.0253052


Mn = 62.22 Kn-m

bd2

= 10809482.9 mm3


d = 207.94 mm

h' = 207.94 mm R= 5.75626h (assume) > h', ok!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.13614

b = -7173558000 2 = 0.00828



As= 703.91 mm

2Final: = 16 mm

()= 16 mm n= 4 bars

(n)= 3.50 bars As= 804.250 mm2


Steel ratio:

max = 0.03163

actual = 0.00946

(governs) min = 0.00508 0.00439 0.00508






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

n =

= 0.851

(^)/

(600/(600+))

=

(10.59/(

^))

=((^24))/2

Mu = = ^2(10.59/(^))


17/198

Design Moment:

(+)Mu= 8 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.14329

b = -7173558000 2 = 0.00112



As= 431.47 mm

2Final: = 16 mm

()= 16 mm n= 4 bars

(n)= 2.15 bars As= 804.250 mm2


Steel ratio:

max = 0.03163

actual = 0.00946

(governs) min = 0.00508 0.00439 0.00508






Vc= 52.54 KN/m




= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

Av(min) = (

2)/4


18/198


Moment Diagram:



As= 804.25 mm2

positive moment

As= 804.25 mm2

negative moment

ln= 3.40 m


---- ---- ---- ---- ---- ---- ----

Negative 2 268.08 66.67 0.102 0.35



s= 82 mm

s > 2db, use case 1 or 2 equation for ld


t= 1

e= 1

s= 1

= 1


ld= 0.44 m

12db= 0.19 m

d= 0.34 m

ld=12/(25()) db

As%= (1)/ x100


s =(2(+)())/(1)


19/198

Beam Details:



8mm



Section:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4

Volume of Sand:Vsand= 0.17 m

3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




1 @ 0.085 m

Rest @ 0.170 m

O.C

Vol =L x W x H


Vol=Vsand x Factor



20/198

*Verify actual to minimize cost


21/198

Right

8mm

0.075 m0.150 m

@ 0.170 m


22/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90 l

u = 0.003

Cover= 60.00 mm


b = 250 mm

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m





Office 2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL= 14.14


Wu= 19.51

Beam RB-3A:

Shear Diagram:



Beam RB-3A - Roof Deck Framing Plan Rating:

Wp2=

Wb=

Wu

Wp1=(

Ws=

L = 7.60 m

Ws + Wp

1

)

Wu = +


23/198

Design For Flexure:

Design Moment:

Mu= 85 KN-m


b = 0.0421753

(desired) = 0.0253052


Mn = 94.44 Kn-m

bd2

= 16407250.83 mm3


d = 256.18 mm

h' = 256.18 mm R= 5.75626h (assume) > h', ok!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.13139

b = -7173558000 2 = 0.01302



As= 1107.00 mm

2Final: = 16 mm

()= 16 mm n= 6 bars

(n)= 5.51 bars As= 1206.374 mm2


Steel ratio:

max = 0.03163

actual = 0.01419

(governs) min = 0.00508 0.00439 0.00508






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

n =

= 0.851

(^)/

(600/(600+))

=

(10.59/(

^))

=((^24))/2

Mu = = ^2(10.59/(^))


24/198

Design Moment:

(+)Mu= 56 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.13614

b = -7173558000 2 = 0.00828



As= 703.91 mm

2Final: = 16 mm

()= 16 mm n= 4 bars

(n)= 3.50 bars As= 804.250 mm2


Steel ratio:

max = 0.03163

actual = 0.00946

(governs) min = 0.00508 0.00439 0.00508






Vc= 52.54 KN/m



Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))


25/198


At Right & Left Support:

= 8 mm

= 0.75 ACI CODE 2010


Vu= 74.10 KN


Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 327.88 mm

say: 325 mm


Vs= 21.75 KN



Xu= 3.8 m

X1 = 1.11 m


Xu= 3.8 m

X2 = 2.45 m


Vs



a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

21.75 135.98


Smax = 170 mm

/=/(1)

/=(0.5)/(2)

0.66(^)bwd

Vs = ()/

0.33(^)bwd

s = (

)/()

, smax /224"

0.33(^)bwd

, smax /424"


26/198


Moment Diagram:

Right

8mm

SAME



As= 804.25 mm2

positive moment

As= 1206.37 mm2

negative moment

ln= 7.20 m


Positive 1 268.08 66.67 0.310 2.23

---- ---- ---- ---- ---- ---- ----

Negative 2 402.12 66.67 0.095 0.68



s= 33 mm



t= 1

e= 1

s =(2(+)())/(1)

As%= (1)/ x100



27/198

Beam Details:



8mm



Section:

Estimate for Beam:


Vol.conc.= 0.720 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 6.48 bags

say: 7

Volume of Sand:

Vsand= 0.36 m

3

say: 1

Volume of Gravel:

Vgravel= 0.72 m3

say: 1

Reinforcing Bars:




Summary: 1 RB-3A

1 @ 0.085 m

Rest @ 0.170 m

O.C

Vol =L x W x H


Vol=Vsand x Factor



28/198


29/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m





Office 2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 14.14


Wu= 19.51

Beam RB-4:

Line of symmetry





1

)

1

Wp2=

Wb=

Wu

l

Wp1=(

Ws=

L = 3.80 m L = 3.80 m

Ws + Wp Wu =Wb +


30/198

Design For Flexure:

Design Moment:

Mu= 28 KN-m


b = 0.0421753

(desired) = 0.0253052


Mn = 31.11 Kn-m

bd2

= 5404741.449 mm3


d = 147.03 mm

h' = 147.04 mm R= 5.75626h (assume) > h', ok!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.14040

b = -7173558000 2 = 0.00401



As= 431.47 mm

2Final: = 16 mm

()= 16 mm n= 3 bars

(n)= 2.15 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

(governs) min = 0.00508 0.00439 0.00508






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

n =

= 0.851

(^)/

(600/(600+))

=

(10.59/(

^))

=((^24))/2

Mu = = ^2(10.59/(^))


31/198

Design Moment:

(+)Mu= 16 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.14215

b = -7173558000 2 = 0.00227



As= 431.47 mm

2Final: = 16 mm

()= 16 mm n= 3 bars

(n)= 2.15 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

(governs) min = 0.00508 0.00439 0.00508






Vc= 52.54 KN/m




= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

Av(min) = (

2)/4


32/198


Moment Diagram:



As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m


---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35



s= 33 mm



t= 1

e= 1

s= 1

= 1


ld= 0.44 m

12db= 0.19 m

d= 0.34 m

ld=12/(25()) db

As%= (1)/ x100


s =(2(+)())/(1)


33/198

Beam Details:



8mm



Section:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4Volume of Sand:

Vsand= 0.17 m3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




1 @ 0.085 m

Rest @ 0.170 m

O.C

Vol =L x W x H


Vol=Vsand x Factor



34/198

Total 3644*Verify actual to minimize cost

Right

8mm

SAME


35/198


36/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m



Office 2.4 9.12


Wu(slab)= 1.2DL + 1.6LL = 28.27

Wu= 30.43

Beam RB-5:

Shear Diagram:




1

)

Wb=

Wu

L = 7.60 m

Ws + Wp

l1

l2

Ws=

Wu =Wb +


37/198

Design For Flexure:

Design Moment:

Mu= 126 KN-m


b = 0.0421753

(desired) = 0.0253052


Mn = 140.00 Kn-m

bd2

= 24321336.52 mm3


d = 311.91 mm

h' = 311.91 mm R= 5.75626h' > h(assume), Revise Section!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.12395

b = -7173558000 2 = 0.02046



As= 1739.47 mm

2Final: = 20 mm

()= 20 mm n= 6 bars

(n)= 5.54 bars As= 1884.960 mm2


Steel ratio:

max = 0.03163

actual = 0.02218

(governs) min = 0.00508 0.00439 0.00508






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

n =

= 0.851

(^)/

(600/(600+))

=

(10.59/(

^))

=((^24))/2

Mu = = ^2(10.59/(^))


38/198

Design Moment:

(+)Mu= 101 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.12861

b = -7173558000 2 = 0.01581



As= 1343.88 mm

2Final: = 20 mm

()= 20 mm n= 5 bars

(n)= 4.28 bars As= 1570.800 mm2


Steel ratio:

max = 0.03163

actual = 0.01848

(governs) min = 0.00508 0.00439 0.00508






Vc= 52.54 KN/m



Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))


39/198


At Right Support:

= 8 mm

= 0.75 ACI CODE 2010


Vu= 113.90 KN


Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 115.22 mm

say: 115 mm


Vs= 61.48 KN



Xu= 3.74 m

X1 = 2.01 m


Xu= 3.74 m

X2 = 2.88 m


Vs



a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

61.48 135.98


Smax = 170 mm

/=/(1)

/=(0.5)/(2)

0.66(^)bwd

Vs = ()/

0.33(^)bwd

s = (

)/()

, smax /224"

0.33(^)bwd

, smax /424"


40/198


At Left Support:

Right = 8 mm

8mm = 0.75 ACI CODE 2010

Factored Shear Force:Vu= 117.40 KN

SAME


Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 109.00 mmsay: 110 mm


Vs= 64.28 KN



Xu= 3.86 m

X1 = 2.13 m



Xu= 3.86 m

X2 = 3.00 m


Vs


Maximum Spacing (smax):a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

64.28 135.98


/=/(1)

/=(0.5)/(2)

0.66(^)bwd

Vs = ()/

0.33(^)bwd

s = (

)/()

, smax /224"

0.33(^)bwd

, smax /424"


41/198

19 @ 0.110 m

Rest @ 0.170 m


Moment Diagram:



As= 1570.80 mm2

positive moment

As= 1884.96 mm2

negative moment

ln= 7.20 m


Positive 1 523.60 66.67 0.260 1.87

---- ---- ---- ---- ---- ---- ----

Negative 2 628.32 66.67 0.095 0.68



s= 27 mm



t= 1

e= 1

s= 1


As%= (As -As1)/As x 100



42/198

Beam Details:



8mm



Section:

Estimate for Beam:


Vol.conc.= 0.720 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 6.48 bags

say: 7

Volume of Sand:

Vsand= 0.36 m

3

say: 1

Volume of Gravel:

Vgravel= 0.72 m3

say: 1

Reinforcing Bars:




Summary: 1 RB-5


1 @ 0.055 m19 @ 0.110 m

Rest @ 0.170 mO.C

1 @18 @

RestO.C

Vol =L x W x H


Vol=Vsand x Factor



43/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m



Office 2.4 9.12


Wu(slab)= 1.2DL + 1.6LL= 28.27

Wu= 30.43

Beam RB-6:


Shear Diagram:




(1+2)

Ws

Wb=

Wu

L = 3.80 m

l1

l2

Ws=

Wu =Wb +

L = 3.80 m


44/198

Design For Flexure:

Design Moment:

Mu= 45 KN-m


b = 0.0421753

(desired) = 0.0253052


Mn = 50.00 Kn-m

bd2

= 8686191.614 mm3


d = 186.40 mm

h' = 186.40 mm R= 5.75626h (assume) > h', ok!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.13785

b = -7173558000 2 = 0.00657



As= 558.63 mm

2Final: = 16 mm

()= 16 mm n= 3 bars

(n)= 2.78 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

(governs) min = 0.00508 0.00439 0.00508






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

n =

= 0.851

(^)/

(600/(600+))

=

(10.59/(

^))

=((^24))/2

Mu = = ^2(10.59/(^))


45/198

Design Moment:

(+)Mu= 25 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 49672157654 1 = 0.14084

b = -7173558000 2 = 0.00357



As= 431.47 mm

2Final: = 16 mm

()= 16 mm n= 3 bars

(n)= 2.15 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

(governs) min = 0.00508 0.00439 0.00508




At Right Support:

Ultimate Shear Moment (Vu)= 52.00 KN/m


Vc= 52.54 KN/m



At Left Support:



Vc= 52.54 KN/m



Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=((^24))/2

Mu = = ^2(10.59/(^))

=0.17(^ ) bwd

=0.17(^ ) bwd


46/198


At Left Support:

= 8 mm

= 0.75 ACI CODE 2010


Vu= 64.00 KN


Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 616.78 mm

say: 420 mm


Vs= 16.83 KN



Xu= 2.1 m

X1 = 0.38 m


Xu= 2.1 m

X2 = 1.24 m


Vs



a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

16.83 135.98


Smax = 170 mm

/=/(1)

/=(0.5)/(2)

0.66(^)bwd

Vs = ()/

0.33(^)bwd

s = (

)/()

, smax /224"

0.33(^)bwd

, smax /424"


47/198


At Right Support:

= 8 mm

= 0.75 ACI CODE 2010Factored Shear Force:

Vu= 52.00 KN


= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mmc.)smax3= 327 mm

Use smax= 170 mm

Actual Spacing (s):

s= 170 mm

First Stirrup:

s1= 85 mm

Stirrups:

1 @ 0.085 m

Rest @ 0.170 m

Av(min) = (

2)/4


48/198


Moment Diagram:



As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m


Positive 1 201.06 66.67 0.260 0.88

---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35



s= 33 mm



t= 1

e= 1


As%= (As -As1)/As x 100Cut-Off= factor x 100


49/198

Beam Details:


Right Left Midspan Right Left

8mm 8mm

1 @ 0.085 m

Rest @ 0.170 m

O.C.



Section:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4

Volume of Sand:

Vsand= 0.17 m

3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




Summary: 2 RB-6


0.055 m0.155 m

@ 0.170 m

Vol =L x W x H


Vol=Vsand x Factor



50/198

(1+2)

Ws


51/198

(governs)


52/198

(governs)


53/198


54/198


55/198


56/198

Right

8mm

Same


57/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm

Assume Section: l1= 0.50 m

b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m

Weight of beam (Wb) 24.00 ---- 1.80

Weight of Slab (Ws1 + Ws2 ) 24.00 ---- 7.20

Wall (Normal weight concrete, Ww1) 21.20 ---- 6.36

Wall (Foam/Plastered Finished, Ww2) ---- 0.48 0.024


Office 2.4 5.76

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 17.86

Wu(wall)= 1.2DL= 7.66

Wu1= 27.68

Wu2= 13.54

Beam B-1:

Line of symmetry


Shear Diagram:

Two-Story office Building

A. Design of Beams

Beam B-1 - 2nd Floor Framing Plan

Date Prepared:

Checked By:

Rating:

Ww2= 1

Wb=

Ww1=()

Wu1=Wb+ Ws+ Ww

Wu2=Wb+Ws2+Ww

Wu1

Ws= (1+2)

L = 7.60 m L = 7.60 m

l1

l2

Wu2Wu1


58/198

Design For Flexure:

Design Moment:

Mu= 25 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 27.78 Kn-m

bd2

= 4825662.01 mm3


d = 138.93 mm

h' = 138.94 mm R= 5.75626

h (assume) > h', ok!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.14084

b = -7173558000 2 = 0.00357



As= 431.47 mm

2Final: = 16 mm

Diam.()= 16 mm n= 3 bars

f bars (n)= 2.15 bars As= 603.187 mm2


Steel ratio:max = 0.03163

actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)




a = 33.31345 mm Strain of steel Yeilds: = 0 001379


beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

)/(0 85^ =/

n =

= 0.851 (^)/(600/(600+))

= (10.59/(^))

=((^24))/2

Mu = = ^2(10.59/(^))


59/198

Design Moment:

(+)Mu= 15 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.14230

b = -7173558000 2 = 0.00212



As= 431.47 mm

2Final: = 16 mm

Diam.()= 16 mm n= 3 bars

f bars (n)= 2.15 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)






Vc= 52.54 KN/m




= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

Av(min) = (

2)/4


60/198


Moment Diagram:



As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m


Positive 1 201.06 66.67 0.260 0.88

---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35



s= 33 mm



t= 1

e= 1

s= 1

= 1



As%= (As -As1)/As x 100



61/198

Beam Details:


Left Midspan Right Left Right

8mm 8mm

1 @ 0.085 m

SAME

Rest @ 0.170 mO.C.



Section:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4

Volume of Sand:

Vsand= 0.17 m3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




Vol =L x W x H


Vol=Vsand x Factor



62/198


63/198


64/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85 l1

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m


Weight of Slab (Ws1+ Ws2) 24.00 ---- 11.40




Office 2.4 9.12

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL= 28.27

Wu(wall)= 1.2DL = 7.66

Wu1= 30.43

Wu2= 23.96

Beam B-2:

Line of symmetry


Shear Diagram:



Beam B-2 - 2nd Floor Framing Plan Rating:

Wb=

Wu1Wu1

Ws= (1+2)

Wu2

L = 7.60 m L = 7.60 m

l2

Ww2= 1

Ww1=()

Wu2=Wb+ Ws1+ Ww

Wu1=Wb+Ws


65/198

Design For Flexure:

Design Moment:

Mu= 134 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 148.89 Kn-m

bd2

= 25865548.4 mm3


d = 321.66 mm

h' = 321.66 mm R= 5.75626

h' > h(assume),Revise Section!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.12237

b = -7173558000 2 = 0.02204



As= 1873.80 mm

2Final: = 20 mm

= 20 mm n= 6 bars

n= 5.96 bars As= 1884.960 mm2



actual = 0.02218

min = 0.00508 0.00439 0.00508 (governs)






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

)/(0 85^ =/

n =

= 0.851 (^)/(600/(600+))

= (10.59/(^))

=((^24))/2

Mu = = ^2(10.59/(^))


66/198

Design Moment:

(+)Mu= 73 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.13340

b = -7173558000 2 = 0.01102



As= 936.41 mm

2Final: = 20 mm

= 20 mm n= 3 bars

n= 2.98 bars As= 942.480 mm2


Steel ratio:

max = 0.03163

actual = 0.01109

min = 0.00508 0.00439 0.00508 (governs)






Vc= 52.54 KN/m



Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))


67/198


At Left Support:

= 8 mm

= 0.75 ACI CODE 2010


Vu= 107.40 KN

Shear Strength in Concrete:Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 128.87 mm

say: 125 mm


Vs= 56.56 KN



Xu= 3.95 m

X1 = 2.02 m



Xu= 3.95 m

X2 = 2.98 m


Vs



a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

56.56 135.98


Smax = 170 mm

Actual Spacing (s):

= -

-

Vs =

s =

, smax d/2

, smax d/4


68/198


69/198


Moment Diagram:



As= 942.48 mm2

positive moment

As= 1884.96 mm2

negative moment

ln= 7.20 m


Positive 1 314.16 66.67 0.260 1.87

---- ---- ---- ---- ---- ---- ----

Negative 2 628.32 66.67 0.102 0.73



s= 27 mm



t= 1

e= 1

s= 1

= 1


ld= 0.82 m


ld=18fyte/(25(fc)) db

As%= (As -As1)/As x 100



70/198

Beam Details:


8mm 8mm



Sections:

Estimate for Beam:Total Volume of Concrete: Class A Mixture: Factor

Vol.conc.= 0.720 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 6.48 bags

say: 7

Volume of Sand:

Vsand= 0.36 m3

say: 1Volume of Gravel:

Vgravel= 0.72 m3

say: 1

Reinforcing Bars:




Summary: 2 B-2


Concrete C 14 220 3080

1 @ 0.065 m

16 @ 0.125 m

Rest @ 0.170 m

1 @ 0.075 m

11 @ 0.150 m

Rest @ 0.170 m

Vol =L x W x H


Vol=Vsand x Factor



71/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85

= 0.90 l

u = 0.003

Cover= 60.00 mm

Assume Section: l= 1.90 m

b = 250 mm

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m


Weight of Slab (Ws) 24.00 ---- 5.7




Office 2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 14.14

Wu(wall)= 1.2DL= 7.66

Wu= 23.96

Beam B-3:

Shear Diagram:




Wb=

Wu

Ws=

L = 3.80 m

Ww2= 1

Ww1=()

Wu =Wb+Ws+Ww


72/198

Design For Flexure:

Design Moment:

Mu= 25 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 27.78 Kn-m

bd2

= 4825662.01 mm3


d = 138.93 mm

h' = 138.94 mm R= 5.75626


Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.14084

b = -7173558000 2 = 0.00357



As= 431.47 mm

2Final: = 16 mm

= 16 mm n= 3 bars

n= 2.15 bars As= 603.187 mm2



actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

)/(0 85^ =/

n =

= 0.851 (^)/(600/(600+))

= (10.59/(^))

=((^24))/2

Mu = = ^2(10.59/(^))


73/198

Design Moment:

(+)Mu= 22 KN-m

Cross Secti 250 mm

b = 340 mm

d = 400 mmh =

Area of Steel: Roots:

4.9672E+10 1 = 0.14128

a = -7173558000 2 = 0.00313

b = 22000000 new = 0.00313 choose the smaller

c = rho new < rho min, use rho min

431.47 mm2

Final: = 16 mm

As= 16 mm n= 3 bars

()= 2.15 bars As= 603.187 mm2

(n)=


Steel ratio: 0.03163

max = 0.00710

actual =

0.00508 0.00439 0.00508 (governs)

min = rho actual > rho min, ok!


Check if Stirrups are neeUltimate Shear Moment (Vu)= 47.50 KN/m


Vc= 52.54 KN/m




= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

Av(min) = (

2)/4


74/198


Moment Diagram:



As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m


Positive 1 201.06 66.67 0.260 0.88

---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35



s= 33 mm



t= 1

e= 1

s= 1

= 1



As%= (As -As1)/As x 100



75/198

Beam Details:



8mm 8mm

1 @ 0.085 m

SAME

Rest @ 0.170 mO.C.



Sections:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4

Volume of Sand:

Vsand= 0.17 m3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




Vol =L x W x H


Vol=Vsand x Factor



76/198


77/198


78/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85 l

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m






Office 2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 14.14

Wu(wall)= 1.2DL= 7.66

Wu= 23.96

Beam B-4:

Line of symmetry


Shear Diagram:




Wb=

Wu

Ws=

L = 3.80 m

Ww2= 1

Ww1=()

L = 3.80 m

Wu =Wb+Ws+Ww


79/198

Design For Flexure:

Design Moment:

Mu= 32 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 35.56 Kn-m

bd2

= 6176847.37 mm3


d = 157.19 mm

h' = 157.19 mm R= 5.75626


Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.13981

b = -7173558000 2 = 0.00461



As= 431.47 mm

2Final: = 16 mm

= 16 mm n= 3 bars

n= 2.15 bars As= 603.187 mm2



actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

)/(0 85^ =/

n =

= 0.851 (^)/(600/(600+))

= (10.59/(^))

=((^24))/2

Mu = = ^2(10.59/(^))


80/198

Design Moment:

(+)Mu= 17 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.14201

b = -7173558000 2 = 0.00241



As= 431.47 mm

2Final: = 16 mm

()= 16 mm n= 3 bars

(n)= 2.15 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)






Vc= 52.54 KN/m




= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

Av(min) = (

2)/4


81/198


Moment Diagram:



As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m


Positive 1 201.06 66.67 0.260 0.88

---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35



s= 33 mm



t= 1

e= 1

s= 1

= 1



As%= (As -As1)/As x 100



82/198

Beam Details:



8mm 8mm

1 @ 0.085 m

SAME

Rest @ 0.170 mO.C.



Section:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4

Volume of Sand:

Vsand= 0.17 m3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




Vol =L x W x H


Vol=Vsand x Factor



83/198


84/198


85/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m


Weight of Slab (Ws1+ Ws2) 24.00 ---- 8.25


Office 2.4 6.6

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 20.46

Wu1= 22.62

Wu2= 12.04

Beam B-5:


Shear Diagram:




Wb=

Wu1Wu2

Ws= (1 + l2)

l1

l2

Wu1= Ws+ Ww

Wu2=Ws2+Ww

L = 7.60 m


86/198

Design For Flexure:

Design Moment:

Mu= 110 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 122.22 Kn-m

bd2

= 21232912.8 mm3


d = 291.43 mm

h' = 291.43 mm R= 5.75626


Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.12698

b = -7173558000 2 = 0.01744



As= 1482.42 mm

2Final: = 20 mm

= 20 mm n= 5 bars

n= 4.72 bars As= 1570.800 mm2



actual = 0.01848

min = 0.00508 0.00439 0.00508 (governs)






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

)/(0 85^ =/

n =

= 0.851 (^)/(600/(600+))

= (10.59/(^))

=((^24))/2

Mu = = ^2(10.59/(^))


87/198

Design Moment:

(+)Mu= 39 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.13876

b = -7173558000 2 = 0.00566



As= 480.96 mm

2Final: = 20 mm

= 20 mm n= 2 bars

n= 1.53 bars As= 628.320 mm2


Steel ratio:

max = 0.03163

actual = 0.00739

min = 0.00508 0.00439 0.00508 (governs)




At Right Support:



Vc= 52.54 KN/m



At Left Support:



Vc= 52.54 KN/m



Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

=0.17(^ ) bwd


88/198


At Left Support:

= 8 mm

= 0.75 ACI CODE 2010


Vu= 69.30 KN

Shear Strength in Concrete:Vc= 70.05 KN

Vc= 52.54 KN

0.5Vc= 26.27 KN


Av= 100.5312 mm2

S= 421.77 mm

say: 420 mm


Vs= 16.83 KN



Xu= 3.8 m

X1 = 0.92 m



Xu= 3.8 m

X2 = 2.36 m


Vs



a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm


Vs

Vs

16.83 135.98


Smax = 170 mm

Actual Spacing (s):

= -

-

Vs =

s =

, smax d/2

, smax d/4


89/198


90/198


Moment Diagram:



As= 628.32 mm2

positive moment

As= 1570.80 mm2 negative moment

ln= 7.20 m


Positive 1 209.44 66.67 0.260 1.87

---- ---- ---- ---- ---- ---- ----

Negative 2 523.60 66.67 0.102 0.73



s= 27 mm



t= 1

e= 1

s= 1

= 1



ld 18f 25(f )) d

As%= (As -As1)/As x 100



91/198

Beam Details:


8mm 8mm

1 @ 0.085 m

SAMERest @ 0.170 m

O.C.



Sections:

Estimate for Beam:Total Volume of Concrete: Class A Mixture: Factor

Vol.conc.= 0.720 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 6.48 bags

say: 7

Volume of Sand:

Vsand= 0.36 m3

say: 1Volume of Gravel:

Vgravel= 0.72 m3

say: 1

Reinforcing Bars:




Summary: 1 B-5


Concrete C 7 220 1540

Vol =L x W x H


Vol=Vsand x Factor



92/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm l2= 1.90 m

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m


Weight of Slab (Ws1 + Ws2 ) 24.00 ---- 11.40




office 2.4 4.56

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DL + 1.6LL = 20.98

Wu(wall)= 1.2DL= 7.66

Wu= 23.96

Beam B-6:

Shear Diagram:




Wb=

Wu

l2

L = 3.80 m

l1

Ww2= 1

Ww1=()

Ws= (1+2)

Wu =Wb+ Ws+ Ww


93/198

Design For Flexure:

Design Moment:

Mu= 24 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 26.67 Kn-m

bd2

= 4632635.53 mm3


d = 136.13 mm

h' = 136.13 mm R= 5.75626


Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.14099

b = -7173558000 2 = 0.00343



As= 431.47 mm

2Final: = 16 mm

= 16 mm n= 3 bars

n= 2.15 bars As= 603.187 mm2



actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)






beam dept(d)


beam depth (d)

bd2=/

desired =0.6

Mn = /

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

a = (

)/(0 85^ =/

n =

= 0.851 (^)/(600/(600+))

= (10.59/(^))

=((^24))/2

Mu = = ^2(10.59/(^))


94/198

Design Moment:

(+)Mu= 19 KN-m


b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.14172

b = -7173558000 2 = 0.00270



As= 431.47 mm

2Final: = 16 mm

()= 16 mm n= 3 bars

(n)= 2.15 bars As= 603.187 mm2


Steel ratio:

max = 0.03163

actual = 0.00710

min = 0.00508 0.00439 0.00508 (governs)






Vc= 52.54 KN/m




= 8 mm

Av min.= 100.5312 mm2


a.) smax1= 170 mm

b.)smax2= 600 mm

c.)smax3= 327 mm

Use smax= 170 mm

Positive Moment

a^2+b+=0

max =0.75

= /

= (0.25(^ ))/

=0.17(^ ) bwd

=((^24))/2

Mu = = ^2(10.59/(^))

Av(min) = (

2)/4


95/198


Moment Diagram:



As= 603.19 mm2

positive moment

As= 603.19 mm2

negative moment

ln= 3.40 m


Positive 1 201.06 66.67 0.260 0.88

---- ---- ---- ---- ---- ---- ----

Negative 2 201.06 66.67 0.102 0.35



s= 33 mm



t= 1

e= 1

s= 1

= 1



As%= (As -As1)/As x 100



96/198

Beam Details:



8mm 8mm

1 @ 0.085 m

SAME

Rest @ 0.170 mO.C.



Sections:

Estimate for Beam:


Vol.conc.= 0.340 m2

Cement (40kg) 9.00

sand 0.50



No.bags= 3.06 bags

say: 4

Volume of Sand:

Vsand= 0.17 m3

say: 1

Volume of Gravel:

Vgravel= 0.34 m3

say: 1

Reinforcing Bars:




Vol =L x W x H


Vol=Vsand x Factor



97/198


98/198


99/198


fy= 275.80 Mpa

f'c= 23.50 Mpa

Es = 200000.00 Mpa

1 = 0.85

= 0.90

u = 0.003

Cover= 60.00 mm


b = 250 mm

d= 240

h = 300 mm

Service Loads:

Dead loads: KN/m3

KN/m2

KN/m



Railings (3" ) 77.30 ---- 5.22


Building corridor/ hall way 3.8 4.75

Ultimate Load: KN/m

Wu(beam)= 1.2DL= 2.16

Wu(slab)= 1.2DLT + 1.6LLT= 12.10

Wu(Railings)= 1.2DL= 6.26

Wu= 20.52

Beam B-7:

Shear Diagram:



Beam B-7- 2nd Floor Framing Plan Rating:

Wb=

Wu

Ws=

Wu =++ Wr

L = 7.60 m

l

Wr=( )


100/198

Design For Flexure:

Design Moment:

Mu= 148 KN-m


b

=0.0421753

(desired) = 0.0253052


Mn = 164.44 Kn-m

bd2

= 28567919.1 mm3


d = 338.04 mm

h' = 338.04 mm R= 5.75626

h' > h(assume),Revise Section!

Final:

b = 250 mm

d = 340 mm

h = 400 mm

Area of Steel:

Roots:

a = 4.9672E+10 1 = 0.11948

b = -7173558000 2 = 0.02494



As= 2119.68 mm

2Final: = 20 mm

= 20 mm n= 8 bars

n= 6.75 bars As= 2513.280 mm2


Steel ra

Documents

Beam & Colum Design - CE 161