STRUCTURAL ANALYSIS AND DESIGN (based on NSCP 2001 Vol. 1 - 5
th
Ed., AISC-ASD, ACI 347)
PROPOSED FALSEWORK DESIGN FOR MOAWA BRIDGE
(Simple Steel Frames with Diagonal Bracings) GENERAL NOTES:
a. Analysis of frame is computed using Staad Pro V07 Analysis Software. Other members subjected subjected to design are considered to be simply supported. b. For beam and column design, consider longitudinal section at centerline. 1. Interior Columns - carries 1 girder load and its components. components. 2. Exterior Columns - carries only ½ of Interior column load and its components. components. Therefore, Design Interior Columns Only. c. Design procedures for adequacy requirements are done by: 1. Staad Pro V07 Program ………………………………………… Code: AISC-Allowable Stress Design Members: H-Beam & Column (W12x65) AISC Steel NSCP 2001-Allowable Stress Design Members: H-Beam & Column (BH300x92) ASEP Steel
2. Detailed Calculation by Hand …………………………. …………………………... (Counter-Cheking) d. Sequence of section investigation and design: 1. Plywood Sheathing (1" thk.) ………………………………… ACI 347 2. Wood Joist (2"x4") @ 200mm O.C………………………….. NSCP-ASD 3. SSP (Type-II) ……………………………………………………… NSCP-ASD NSCP/AISC-ASD 4. H-Beam as Girders (300x300mm) NSCP/AISC-ASD 5. H-Beam as Columns (350x350mm) Note: USE 300x300mm section in design design consideration.
e. Lateral Loads are to be neglected in the design. However, provide bracing supports for the frame, especially especially on the transverse section if in case there are lateral forces that may occur.
DESIGN CRITERIA and SPECIFICATIONS
I. LIVE LOADS Sect. 205.3.4, T205-2, Pg.2-9 a. Liveload (Special Loads for Construction)…………………………… 7.20 KPa II. DEAD LOADS a. Concrete ……………………………………………………………………… 24.00 KN/m³ Sect. 204.2, T204-1, Pg.2-5 b. Steel Materials……………………………………………………………… 77.30 KN/m³ Sect. 204.2, T204-1, Pg.2-5 c. Steel Forms ……………………………………………………………….. 9.000 KPa d. Wood Bracings……………………………………...………………………. 1.400 KPa e. Formworks (includes pylwood & joists) ……………………………… 1.200 KPa IV. ALLOWABLE STRESSES a. Structural Steel Materials 276.0 Mpa DESIGN SCHEME:
STEEL and WOOD SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
Bridge Name: Moawa Bridge, Bohol Length of Bridge: 32.0 m Span Length: 3.6m to accommodate 9-pcs of SSP per span [Falsework] INPUT DATA and DESIGN CRITERIA Prestressed I-Girder = Area
(Total) =
Girder Width =
γ(Unit Weight) = γ(Linear Weight) = ow. deflection = Allow. ðdeflection =
Type IV-B AASHTO Specs 0.6123 m² AASHTO Specs 0.661 m AASHTO Specs 24.024 KN/m³ 153 lb/ft³ 14.710 KN/m 1008 lb/ft L/180 Timber L/360 Steel
DEAD LOADS: Steel Forms = Wood Bracings = Concrete = Formwork = Sub-Total =
Kpa 9.000 1.400 22.25 1.200 33.850
psf 188.03 29.25 464.86 25.07 707.21
LIVELOADS: Working Load = 7.200 150.4
KN/m 5.95 0.93 14.71 [Plywood & Joist] [Girder Components]
[Special Loads]
I. DESIGN OF SHEATHING Material Properties: Source: (ACI 347 Table 4-2,4-3) Plywood = Bending, Fb = Shearing, Fv = E= S = I= Ib/Q = spacing, s = Support =
1.0" thk 10.7 Mpa 0.39 Mpa 10,345 Mpa 10,881 mm³ 176,066 mm^4
5,730 mm² 0.204 m 3 or more spans
1545 Psi 57 Psi 1500000 Psi 0.664 in³ 0.423 in^4 8.882 in² [(0.661-0.050)/3] 8.03 in
Loadings: (Consider 1-ft strip of plywood) DL = 707.21 psf = 707.21 lb/ft LL = 150.43 psf = 150.43 lb/ft
wu = 857.6 lb/ft
0.661
s
s
s
Loading Combination: (NSCP Sect. 203.3.1 - ASD)
Wu = (DL + LL) = 857.640 lb/ft
[self-weight included]
From ACI 347 Using Table 7-1 (Safe Spacing of Supports) Spacings Bending, Fb Rolling Shear, Fv ∆=l/360 ∆=1/16" (20FvS/wu)(Ib/Q)+1.5 1.69 √(EI/wu) 3.23 √(EI/wu) 10.95 √(FbS/wu) (in.) Max. Spacing 11.98 in 9.34 in 15.29 in 16.85 in Actual Spacing 8.03 in 8.03 in 8.03 in 8.03 in Check Act. < All Act. < All Act. < All Act. < All Status [Adequate] [Adequate] [Adequate] [Adequate] Therefore USE: Ordinary Plywood (1.0" thk) with Joist spaced @ 200mm O.C. Note: Failure on Plywood if we use t=1/2" or even 3/4" with joist spaced @ 200mm O.C.
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
TABLE 7-1
II. DESIGN OF WOOD JOIST Material Properties: Source: (website: www.supertimber.com) Coco Timber = b= d= Bending, Fb = Shearing, Fv = E= S = I= Ib/Q = Unit Weig t, γ = spacing, s = assumed length, L = selfweight = Support =
2" x 4" 50.000 mm 100.00 mm 13.1 Mpa 1.30 Mpa 3,100 Mpa 83,333 mm³ 4,166,667 mm^4
3,333 mm² 4.33 KN/m³ 0.204 m 0.400 m 0.022 KN/m 3 or more spans
1900 psi 189 psi 449500 psi 5.085 in³ 10.010 in^4 5.166 in² 441 Kg/m³ 8.03 in 15.74 in
s
s
0.40
s
0.40
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 ) Loadings:
Loading Combination: (NSCP Sect. 203.3.1 - ASD) DL = = LL = =
33.85 Kpa 6.905 KN/m 7.20 Kpa 0.158 KN/m
wu = Mu = Vu = ð ACT =
7.063 KN/m 0.141 KN-m 1.413 KN 0.182 mm
(DL)(s) Wu = (DL + LL) = 7.063 KN/m
(LL)(s) [including self-weight] 1/8(Wu)(L²) ½(Wu)(L) 5 384
WL
4
EI
Bending, Fb Shearing, Fv Deflection, ð 6M/bd² 3V/2A (5WuL )/384EI Actual 1.692 MPa 0.424 MPa 0.182 mm Allowable 13.100 MPa 1.300 MPa 2.22 mm Check Act. < All Act. < All Act. < All Status ADEQUATE ADEQUATE ADEQUATE Therefore USE: Wood Joist 50x100mm (2" x 4") @ 200mm O.C. Note: Not critical as long as SSP are placed side by side with no gaps. Stresses
III. DESIGN OF SSP Type-II (Deck Flooring) Material Properties: Source: Sumitomo SKSP Steel Sheet Piles Note: As per one (1) ssp SSP = b= d= t= A = fy = Allow. Bending, Fb = Allow. Shearing, Fv = E= S = I= Unit Weig t, γ =
Type II 400 mm 100 mm 10.50 mm 6,118 mm² 276.0 Mpa 82.8 Mpa 55.2 Mpa 200,000 Mpa 152,000 mm³
0.60fy (50% Eff.) 0.40fy (50% Eff.)
0.40
0.40
12,400,000 mm^4
0.47 KN/m³ span length, L = 2.250 m selfweight = 0.003 KN/m Widthgirder = 0.661 m
Loadings: Girder Components = (Girder)(Wgirder)(s) ÷ 9pcs
= (33.85)(0.661)(3.6)÷ 9pcs = 8.950 KN Selfweight =
Tributary Area: Span Length, L = Span Spacing, s =
2.250 m 3.600 m
(γ)(Area)(L)
= (0.47)(0.006118)(2.25) = 0.006 KN DL = 8.956 KN [per ssp] Live Load = (LL)(L)(s) ÷ 9pcs = (7.2)(2.25)(3.6)÷ 9pcs LL = 6.480 KN [per ssp]
Pu
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 ) Summary:
Loading Combination: (NSCP Sect. 203.3.1 - ASD) DL = 8.956 KN LL = 6.480 KN
Pu = Mu = Vu = ACT =
Pu = (DL + LL) = 15.436 KN
15.436 KN 8.683 KN-m 7.718 KN 1.477 mm
[self-weight included as per (1) ssp] Pu L / 4 Pu / 2 Pu L³ / 48EI Bending, Fb Shearing, Fv Deflection, ð Mu / Sx Vu / A Pu L³ / 48EI 57.125 MPa 1.262 MPa 1.477 mm 82.800 MPa 55.200 MPa 6.250 mm Act. < All Act. < All Act. < All ADEQUATE ADEQUATE ADEQUATE USE: SSP Type-II for Deck Flooring placed side by side.
Stresses Actual Allowable Check Status Therefore
IV. DESIGN OF GIRDERS (H-Beam 300x300) Material Section and Properties: Source: (ASEP Steel Handbook 1994)
y-axis
Built-Up Shape = A = d= tw = bf = tf = Linear γ = w= k (crippling use) =
BH 300 x 92 11,744 300 8.00 300 12.00 0.904 7.00 19.00
Flange Width-Thickness Ratio mm² bf/2tf = 12.50 mm mm Web Depth-Thickness Ratio mm d/tw = 37.50 mm KN/m [92.19] kg/m mm [t f + w] mm
rx = ry = rt = Sx = Sy = Ix = Iy = E= fy =
132.60 78.30 83.50 1,377,000 480,000 207,000,000 72,000,000 200,000 276
mm mm mm mm³ mm³ mm 4 mm Mpa Mpa
3,600.00 3,600.00
mm mm
Span Length, L = Un-Supported , Lb =
43.11
mm
0 0 3
x-axis
= d
tw =8
bf = 300
4
[simply supported]
Length, Lc = min { [200bf / fy] , [137900 / (fyd ÷ bf tf )] } = 3,611.58 mm L / rT =
tf =12
[Actual Un-Braced Length in Bending] [Max. Un-Braced Length of Compression]
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
Determine Allowable Bending Stress, Fb: Determine Allowable Shearing Stress, Fv: COMPACT Requirements
a. (bf/2tf) ≤ (170/√ fy) 12.50 b.
≤
≤
3,600.00
≤
a.
YES
(bf/2tf) ≤ (250/√ fy)
YES
12.50 YES
≤
3,600.00
≤
N/A
≥
NO
3611.58
b. If Stress in Tension
15.05
N/A
Fb = 0.60fy YES
c. If Stress in Compression
3611.58
N/A
Fb = max (x,y,z)
d. If a,b & c =YES d. USE Fb = 0.66fy
Lb ≥ Lc
a. 3,600.00
Lb ≤ Lc
c.
3611.58
COMPACT or NON-COMPACT Requirements [USE: min of b,c]
(bf/2tf) ≥ (170/√ fy) 12.50 10.23 ≥
b.
YES
101.12
Lb ≤ Lc
c.
NO
10.23
(d/tw) ≤ (1680/√ fy) 37.5
NON-COMPACT Requirements Fb = 165.60
Fb=min(x,y)
165.6
x = 0.60fy
(x) When 703,270Cb ≤ L/rt ≤ ≤≤3,516,330Cb fy fy
N/A
=fy{2/3 - [fy(L/rt)² / 10.55e6 Cb]}
y =fy [0.79 - 0.000762 (bf/2tf) √fy]
(y) When L/rt >
3,516,330Cb fy
N/A
=(1,172,100 Cb) / (L/rt)²
RESULTS: Fb = 165.60 MPa Fv = 110.40 MPa
(z) For Any Value of L/rt =(82,740 Cb) / (Ld ÷ bf tf )
[see table] [0.40fy]
Note: Cb=1.75+(1.05M1 /M2)+0.30(M1 /M2)² ≤ 2.3 USE: Cb=1.0 [Conservative Value]
Loadings: Girder = g r er = = SSP = = = Selfweight =
ea
= = oa (TOTAL) =
Tributary Area: girder =
0.661 m
Span Length, L = Span Spacing, s =
3.600 m 2.250 m
girder
(33.85)(0.661) 22.375 KN/m (γ)(s)(Assp)(9.0 pcs) ÷ L (0.47)(2.25)(0.006118)(9.0 pcs) ÷ 3.6 0.016 KN/m (γlinear)(L) (0.904)(3.6) 3.254 KN/m 25.645 KN/m
LL = (LL)(s) = (7.2)(2.25) Live Load (TOTAL) = 16.200 KN/m Summary:
Loading Combination: (NSCP Sect. 203.3.1 - ASD) DL = 25.645 KN/m LL = 16.200 KN/m
wu = Mu = Vu = ACT =
41.85 KN/m 51.520 KN-m 87.120 KN 2.211 mm
N/A
Wu = (DL + LL) = 41.845 KN/m [self-weight included] [see Staad Pro. V7 analysis results] [see Staad Pro. V7 analysis results] 4
(5/384) (WuL / EI)
Beam No. 1 Beam No. 1
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
Stresses Actual Allowable Check Status Therefore
Bending, Fb Shearing, Fv Deflection, ð (5Wu L )/384EI Mu / Sx Vu / d tw 37.415 MPa 36.300 MPa 2.211 mm 165.600 MPa 110.400 MPa 10.000 mm Act. < All Act. < All Act. < All ADEQUATE ADEQUATE ADEQUATE USE: H-Beam (300x300) as Girder spaced @ 2.250m O.C.
Check: Local Web Yielding and Web Crippling
Stresses
R (actual) = 87.120 KN
N = 300
R/[tw(N+5k)]
R/[tw(N+2.5k)]
R = 177.2 (factor)
R = 89.3 (factor)
d from end>d
d from end ≤ d
d from end>d
d from end ≤ d
K = 19 Factor
tw²[1+3(N/d)(tw /tf )
1.5
dist. = 0.0 N/A USE N/A USE Results 31.338 MPa 237.181 KN x √(Fyw tf / tw) Allowable = (0.66fy) 182.160 MPa 87.120 KN Check Act. < All Act. < All 2.656 KN Status ADEQUATE ADEQUATE Therefore USE: H-Beam (300x300) as Girder spaced @ 2.250m O.C. Note: PROVIDE adequate connection to steel pile caps. (Welding C onnection)
V. DESIGN OF STEEL BEAM USED AS COLUMN SUPPORT Material Section and Properties: Source: (ASEP Steel Handbook 1994) Built-Up Shape = A = d= tw = bf = tf = Linear γ =
BH 300 x 92 11,744 300 8.00 300 12.00 0.904
y-axis
Flange Width-Thickness Ratio bf/2tf = 12.50
mm² mm mm Web Depth-Thickness Ratio mm d/tw = 37.50 mm KN/m [92.19] kg/m
rx = 132.60 mm ry = 78.30 mm rt = 83.50 mm Sx = 1,377,000 mm³ Sy = 480,000 mm³ Ix = 207,000,000 mm4 4 Iy = 72,000,000 mm E= 200,000 Mpa fy = 276 Mpa Column Length, L = 6,000 mm Un-Supported , Lb = 6,000 mm Length, Lc = min { [200bf / fy] , [137900 / (fyd ÷ bf tf )] } = 3,611.58 mm Select Type = (c) see NSCP Table 1.2 see NSCP Table Length Factor, k = kL / r t = 86.2275 Cc = √ (2 π² E / fy) = 119.598 CHECK: Slenderness Ratio Requirements (Main Compression Member) r t = 200 ≤ 200 [OK] 86.23 ≤
tf =12 0 0 3
x-axis [strong axis]
= d
tw =8
bf = 300
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
Determine Allowable Bending Stress, Fb: Determine Allowable Shearing Stress, Fv: COMPACT Requirements
NON-COMPACT Requirements
a. (bf/2tf) ≤ (170/√ fy) 12.50
≤
37.5
≤
6,000.00
≤
(bf/2tf) ≥ (170/√ fy) 12.50 10.23 ≥
YES
(bf/2tf) ≤ (250/√ fy)
YES
b.
YES
101.12
12.50 NO
Lb ≤ Lc
c.
a.
10.23
(d/tw) ≤ (1680/√ fy)
b.
NO
≤
6,000.00
≤
6,000.00
N/A
NO
165.60
c. If Stress in Compression
165.48
Fb = max (x,y,z)
N/A
x = 0.60fy
3611.58
b. If Stress in Tension
3611.58
Fb=min(x,y)
≥
YES
Fb = 0.60fy
d. If a,b & c =YES d. USE Fb = 0.66fy
Lb ≥ Lc
a.
15.05
Lb ≤ Lc
c.
3611.58
COMPACT or NON-COMPACT Requirements [USE: min of b,c] Fb = 165.48
(x) When 703,270Cb ≤ L/rt ≤ ≤≤3,516,330Cb 130.31 fy fy 6
y =fy [0.79 - 0.000762 (bf/2tf) √fy]
=fy{2/3 - [fy(L/rt)² / 10.55e Cb]} (y) When L/rt >
3,516,330Cb fy
N/A
=(1,172,100 Cb) / (L/rt)²
RESULTS: Fb = 165.48 MPa Fv = 110.40 MPa
(z) For Any Value of L/rt =(82,740 Cb) / (Ld ÷ bf tf )
[see table] [0.40fy]
Note: Cb=1.75+(1.05M1 /M2)+0.30(M1 /M2)² ≤ 2.3 USE: Cb=1.0 [Conservative Value]
Determine Allowable Axial Stress, Fa: FS = 5/3 + 3(KL/r) - (KL/r)³ 8Cc 8Cc³
=
1.89
Since, kL/rt
[<]
Cc
Therefore, When kL/r < Cc [Short-Columns] Fa = {1 - [(kL/r)² ÷ 2 Cc²]} x fy / FS = 108.065 Mpa
USE:
When kL/r > Cc [Long Column] Fa = (12 π² E) / [23 (kL/r)²] = N/A
Fa = 108.065 MPa
Pu = Selfweight = Pile Cap Weights = Accecories = Total Pu =
163.640 KN 5.424 KN 2.034 KN 1.636 KN 172.734 KN
[see Staad Pro. V8i analysis results] [(Linear γ)(Length of Column)] [(Linear γ)(Length of Beam)] (Assume 1% of Pu)
Column No. 8
Mu = 2.810 KN-m fa = 14.708 Mpa fb = 0.006 Mpa
[see Staad Pro. V07 analysis results] [Pu / A] Actual Compressive Stress [Mu / Sx] Actual Bending Stress
Column No. 8
Summary:
fa = 14.708 Mpa Fa = 108.065 Mpa
165.48
fb = 0.006 Mpa Fb = 165.480 Mpa
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
(fa / Fa) = 0.14 Check
(fa / Fa) ≤ 0.15
(fa / Fa) > 0.15
Requirements Governs
Requirements N/A
Interaction Value Check
0.136
Status
SAFE
Therefore
≤ 1.0 Columns Section is Adequate for Both Bending and Compression
CHECK Shearing Stress for Columns: Vu = 0.690 KN v = 0.288 Mpa Fv = 110.400 Mpa Check = [fv < Fv]
[see Staad Pro. V07 analysis results] [Vu / d tw] u tw [Satisfactory]
STAAD PRO V2007 ANALYSIS wu = 41.850 KN/m
[from Design IV-Steel Beam Design]
References: (interaction)
when ≤ 0.15 (fa/Fa)+(fb/Fb) ≤ 1.0 when > 0.15 fa + Cm fb ≤ 1.0 Fa (1-fa/Fe') Fb
Cm=0.60-0.4M1/M2 ≤ 0.4 Cm =0.85 (sidesway) = 0.85 Fe'=(1030000) / (KL/r)² =138.53
STEEL SECTION DESIGN and INVESTIGATION PCDG Formwork and Falsework (Based on NSCP 2001 Vol. 1, 5th Edition and ACI 347 )
MOMENT DIAGRAM
SHEAR DIAGRAM
AXIAL FORCES
