ANALYSIS AND DESIGN OF BEAM -SRB

DESCRIPTION : FTB-1 LEVEL : FOUNDATION Code : ACI 318-05 and NSCP 2010
Beam Material and Specifications : FORMULAS :
fc' = 21 Mpa compressive strength - concrete Mu = f'c b d w (1-0.59w) : eq. for singly-reinforced member
fy = 275 Mpa yield strength - steel flexure fVc = (0.17(fc'))/bwd : shear cap. of unreinforced concrete
fy (sec.) = 275 Mpa yield strength - steel shear Vs = (Vu/ - fVc ) : shear cap. of steel
Main Bar 16 mm main rebar diameter Av/ s = Vs / (fyv d) : shear reinforcement
Conc. Cover 40 mm concrete cover At / s = Tu / (2 f Ao fyv cot q) : torsion reinforcement
Stirrups 10 mm secondary rein. Size Tcr = 1.06 f (fc')1/2(Acp2 / Pcp) : threshold torsion
h= 400 mm total depth of beam Acp = b x h : gross area of section
b= 200 mm beam width Pcp = 2xb + 2xh : gross perimeter of section
d= 342 mm effective depth Al = (At/s)Ph (fyv / fyl)cot2q : add. longitudinal steel due to torsion
s= 25 mm clear sp.of bars for double layer rein. w = 0.0132fs(3(dcA)) : crack width
A.) End Section Beam Flexural Design Cross Section Detail
Mu= 13 KN-m Double Layer Reinforcement YES
Ru= 0.595150 Bars @ 2nd Layer = 2 use 5 pcs. - 16 mm Top Bars
rho = 0.002202 d' = 301 mm Clear spacing = 26 mm OK!
Ductility Check

rho bal. = 0.037833 d= 342 mm

rho min. = 0.005091 a = 77.439818912 mm
rho max. = 0.028375 Mu = 45.276224611 KN - m
Use rho = 0.005091 Mu= 26.103597875 KN - m
As = 348 mm Mu cap = 71.379822485 KN - m
No. of Bars 1.732 F. S. = Mu (cap) / Mu (act.)
Say 3 pcs. = 5.696713686 OK! use 2 pcs. - 16 mm Bottom Bars
4 Ductility Check = 0.01469751 OK!

B.) Mid Span Section Beam Flexural Design Cross Section Detail
Mu= 24 KN-m Double Layer Reinforcement YES
Ru= 1.123328 Bars @ 2nd Layer = 2
rho = 0.004222 d' = 301 mm use 2 pcs. - 16 mm Top Bars
Ductility Check

rho bal. = 0.037833 d= 342 mm

rho min. = 0.005091 a = 61.95185513 mm
rho max. = 0.028375 Mu = 30.954874613 KN - m
Use rho = 0.005091 Mu= 26.874322747 KN - m
As = 348 mm Mu cap = 57.829197359 KN - m
No. of Bars 1.732 F. S. = Mu (cap) / Mu (act.) use 4 pcs. - 16 mm Bot. Bars
Say 2 pcs. = 2.4452091907 OK! Clear spacing = 68 mm OK!
3 Ductility Check = 0.01175801 OK!

C.) Shear Reinforcement Design Section Detail

STIRRUPS MAIN BARS

Shear Reinforcement Properties and Loadings
Shear Reinforcement
Description Vu (Kn) bw (mm) d (mm)
pcs. size
Max. Pos. 2 10 21.48 200 342 1
Max. Neg. 2 10 1.42 200 342 1

Shear Reinforcement Design

Shear Capacity
Description Req. S. Max S. Sp. d/2 USE:
Vc Vs
Max. Pos. 53.29 N/A N/A 300 85.5 N/A Note: N/A Value means that Shear Reinforcement is not necessary for the section
Max. Neg. 53.29 N/A N/A 300 85.5 N/A same as Torsion Reinforcement.

D.) Crack Control Check E.) Tortional Reinforcement Check

End Section Forces Crack Width Check Tortional Strength Limit

Description fs=0.6fy dcp At w all. w act. Remark Description Tu V (Av/S) T (At/S) Crack Torque Tu'
Top bars 165 74.4 5952 0.4 0.16601086 OK Max Pos. 3.15 N/A 0.23 6.92
Bot. bars 165 58 11600 0.4 0.19084753 OK Max. Neg. 3.15 N/A 0.23 6.92

Mid Span Section Forces Crack Width Check Required Spacing

Description fs=0.6fy dcp A w all. w act. Remark Description (Tu'/4) S req. S min. S max. USE:
Top bars 165 58 11600 0.4 0.19084753 OK Max Pos. 1.73 N/A 19.04 105.00 N/A
Bot. bars 165 78.5 7850 0.4 0.18534078 OK Max. Neg. 1.73 N/A 19.04 105.00 N/A

Exposure type = 0.4 For Interior Members Acp = xy area enclosed by outside perimeter 80000
dcp = Distance of tension surface to centroid of reinforcements Pcp = 2x + 2y outside perimeter of concrete x-sec. 1200
At = 2*dcp*bw/(no. of bars) - Effective Tension Area Ph = 2(x1 + y1) perimeter of concrete area 840
 ANALYSIS AND DESIGN OF BEAM -DRB
DESCRIPTION : B-1 LEVEL : - Code : ACI 318-05 and NSCP 2010
Beam Material and Specifications : FORMULAS :
fc' = 21 Mpa compressive strength - concrete Mu = f'c b d w (1-0.59w) : eq. for singly-reinforced member
fy = 275 Mpa yield strength - steel flexure fVc = (0.17(fc'))/bwd : shear cap. of unreinforced concrete
fy (sec.) = 275 Mpa yield strength - steel shear Vs = (Vu/ - fVc ) : shear cap. of steel
Main Bar 16 mm main rebar diameter Av/ s = Vs / (fyv d) : shear reinforcement
Conc. Cover 40 mm concrete cover At / s = Tu / (2 f Ao fyv cot q) : torsion reinforcement
Stirrups 10 mm secondary rein. Size Tcr = 1.06 f (fc')1/2(Acp2 / Pcp) : threshold torsion
h= 400 mm total depth of beam Acp = b x h : gross area of section
b= 300 mm beam width Pcp = 2xb + 2xh : gross perimeter of section
d= 342 mm effective depth Al = (At/s)Ph (fyv / fyl)cot2q : add. longitudinal steel due to torsion
s= 25 mm clear sp.of bars for double layer rein. w = 0.0132fs(3(dcA)) : crack width
A.) DOUBLY REINFORCED - End Section Beam Flexural Design Cross Section Detail
Mu= 13 KN-m quadratic constants (A,B,C,) 2 Layers NO
d' = 58 A= 4551.75 1 Bars use 3 - pcs. - 16 mm Top Bars Where:
b1 = 0.85 B = 196035.38158 2 Bars Clear spacing = 76 mm OK!
As1 = 0 C = -20990865.474 Mu= Actual moment
As2 = 603.185789489 c = 49.707208581 mm Mu1= Moment for Tension
As = 603.185789489 a = 42.2511272934 mm Mu1= Moment for 2nd Layer
AsT = -1657.1093881 Mu1 = 47.902857804 KN - m Reinforcement
As' = -1657.1093881 Mu'1 = 0 KN - m Mu2= Moment for Compression
fs = 3528.17387779 Mu2 = -15.432794326 KN - m use 3 - pcs. - 16 mm Bottom Bars Reinforcement
fs' = -100.09966349 Mu = 32.470063478 KN - m Clear spacing = 76 mm OK! As1= Area of Reinforcement
As(Tension)= 3 Bars F. S. = Mu (cap) / Mu (act.) for Tension
As'(Comp)= 3 Bars F. S. = 2.5913857524 OK! As2= Area of Reinforcement
for Compression
B.) DOUBLY REINFORCED - Mid Span Section Beam Flexural Design Cross Section Detail fs= Steel Stress for Tension
Mu= 24 KN-m quadratic constants (A,B,C,) 2 Layers NO Reinforcement
d' = 58.00 A= 4551.75 1 Bars use 3 - pcs. - 16 mm Top Bars fs'= Steel Stress for Compression
b1 = 0.85 B = 196035.38158 2 Bars Clear spacing = 76 mm OK! Reinforcement
As1 = 0.00 C = -20990865.474 F.S.= Factor of Safety w/c is
As2 = 603.19 c = 49.707208581 mm Capacity / Demand Ratio
As = 603.19 a = 42.2511272934 mm and Should not be less than
AsT = -1657.11 Mu1 = 47.902857804 KN - m or equal to 1
As' = -1657.11 Mu'1 = 0 KN - m
fs = 3528.17 Mu2 = -15.432794326 KN - m use 3 - pcs. - 16 mm Bot. Bars Note:
fs' = -100.10 Mu = 32.470063478 KN - m Clear spacing = 76 mm OK! for spacing N.G. stands for
As(Tension)= 3 Bars F. S. = Mu (cap) / Mu (act.) "Not Good"
As'(Comp)= 3 Bars F. S. = 1.3729413733 OK!

C.) Shear Reinforcement Design Section Detail

STIRRUPS MAIN BARS

Shear Reinforcement Properties and Loadings
Shear Reinforcement
Description Vu (Kn) bw (mm) d (mm)
pcs. size
Max. Pos. 2 10 21.48 300 342 1
Max. Neg. 2 10 1.42 300 342 1

Shear Reinforcement Design

Shear Capacity
Description Req. S. Max S. Sp. d/2 USE:
Vc Vs
Max. Pos. 79.93 N/A N/A 300 85.5 N/A Note: N/A Value means that Shear Reinforcement is not necessary for the section
Max. Neg. 79.93 N/A N/A 300 85.5 N/A same as Torsion Reinforcement.

D.) Crack Control Check E.) Tortional Reinforcement Check

End Section Forces Crack Width Check Tortional Strength Limit

Description fs=0.6fy dcp At w all. w act. Remark Description Tu V (Av/S) T (At/S) Crack Torque Tu'
Top bars 165 58 11600 0.4 0.19084753 OK Max Pos. 3.15 N/A 0.12 13.35
Bot. bars 165 58 11600 0.4 0.19084753 OK Max. Neg. 3.15 N/A 0.12 13.35

Mid Span Section Forces Crack Width Check Required Spacing

Description fs=0.6fy dcp A w all. w act. Remark Description (Tu'/4) S req. S min. S max. USE:
Top bars 165 58 11600 0.4 0.19084753 OK Max Pos. 3.34 N/A 28.56 130.00 N/A
Bot. bars 165 58 11600 0.4 0.19084753 OK Max. Neg. 3.34 N/A 28.56 130.00 N/A

Exposure type = 0.4 For Interior Members Acp = xy area enclosed by outside perimeter 120000
dcp = Distance of tension surface to centroid of reinforcements Pcp = 2x + 2y outside perimeter of concrete x-sec. 1400
At = 2*dcp*bw/(no. of bars) - Effective Tension Area Ph = 2(x1 + y1) perimeter of concrete area 1040
 Beam L/C Node Fx kN Fy kN Fz kN Mx kNm
Max Fx 15 201 1.2DL 5 26.82 9.43 -0.23 -0.39
Min Fx 1 201 1.2DL 1 1.33 21.48 0.11 -3.15
Max Fy 1 201 1.2DL 1 1.33 21.48 0.11 -3.15
Min Fy 17 201 1.2DL 13 23.36 1.42 -0.12 -0.36
Max Fz 19 201 1.2DL 10 26.82 9.43 0.23 0.39
Min Fz 15 201 1.2DL 5 26.82 9.43 -0.23 -0.39
Max Mx 5 201 1.2DL 6 1.33 21.48 -0.11 3.15
Min Mx 1 201 1.2DL 1 1.33 21.48 0.11 -3.15
Max My 15 201 1.2DL 5 26.82 9.43 -0.23 -0.39
Min My 19 201 1.2DL 10 26.82 9.43 0.23 0.39
Max Mz 1 201 1.2DL 1 1.33 21.48 0.11 -3.15
Min Mz 1 201 1.2DL 2 1.33 14.7 0.11 -3.15
My kNm Mz kNm
0.49 7.53
-0.09 12.53
-0.09 12.53
0.1 -6.36
-0.49 7.53
0.49 7.53
0.09 12.53
-0.09 12.53
0.49 7.53
-0.49 7.53
-0.09 12.53
0.13 -23.65
 Beam L/C Node Fx kN Fy kN Fz kN
Max Fx 15 201 1.2DL 5 98.86 22.24 -0.29
Min Fx 1 201 1.2DL 1 11.95 63.31 0.76
Max Fy 1 201 1.2DL 1 11.95 63.31 0.76
Min Fy 17 201 1.2DL 13 88.33 11.11 0.04
Max Fz 1 201 1.2DL 1 11.95 63.31 0.76
Min Fz 5 201 1.2DL 6 11.95 63.31 -0.76
Max Mx 5 201 1.2DL 6 11.95 63.31 -0.76
Min Mx 1 201 1.2DL 1 11.95 63.31 0.76
Max My 15 201 1.2DL 5 98.86 22.24 -0.29
Min My 19 201 1.2DL 10 98.86 22.24 0.29
Max Mz 1 201 1.2DL 1 11.95 63.31 0.76
Min Mz 1 201 1.2DL 2 11.95 56.52 0.76
Mx kNm My kNm Mz kNm
-1.48 1.25 18.7
-10.47 -0.6 39.55
-10.47 -0.6 39.55
-1.47 0.87 -22.58
-10.47 -0.6 39.55
10.47 0.6 39.55
10.47 0.6 39.55
-10.47 -0.6 39.55
-1.48 1.25 18.7
1.48 -1.25 18.7
-10.47 -0.6 39.55
-10.47 0.93 -80.28