multiple-support response spectrum analysis of the golden gate bridge
Bridge Support 1
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Transcript of Bridge Support 1
STAAD SPACESTART JOB INFORMATIONENGINEER DATE 18-Jul-15END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES1 0 0 0; 2 2 0 0; 3 2 0 4.8; 4 0 0 4.8; 5 0 11 0; 6 2 11 0; 7 2 11 4.8;8 0 11 4.8; 9 0 1 0; 10 2 1 0; 11 2 1 4.8; 12 0 1 4.8; 13 0 6 0; 14 2 6 0;15 2 6 4.8; 16 0 6 4.8; 17 0 11 -2; 18 2 11 -2; 19 2 11 6.8; 20 0 11 6.8;21 2 11 1.6; 22 2 11 3.2; 23 0 11 3.2; 24 0 11 1.6;MEMBER INCIDENCES5 1 9; 6 2 10; 7 3 11; 8 4 12; 9 5 6; 10 6 21; 11 7 8; 12 8 23; 13 9 13;14 10 14; 15 11 15; 16 12 16; 21 13 14; 22 16 15; 23 13 16; 24 14 15; 25 9 10;26 12 11; 27 9 12; 28 10 11; 29 6 15; 30 7 14; 31 14 11; 32 15 10; 33 5 16;34 8 13; 35 13 12; 36 16 9; 37 6 13; 38 5 14; 39 14 9; 40 13 10; 41 8 15;42 7 16; 43 16 11; 44 15 12; 45 5 17; 46 6 18; 47 7 19; 48 8 20; 49 17 18;50 20 19; 51 21 22; 52 22 7; 53 23 24; 54 24 5; 55 24 21; 56 23 22; 57 18 14;58 17 13; 59 19 15; 60 20 16; 65 13 5; 66 14 6; 67 15 7; 68 16 8;START GROUP DEFINITIONMEMBER_BZ-1 10 12 45 TO 48 51 TO 54_BX-1 9 11 49 50 55 56_BZ-2 23 24 27 28_BX-2 21 22 25 26_DS-1 57 TO 60_COL 5 TO 8 13 TO 16_CBZ 29 TO 36_CBX 37 TO 44END GROUP DEFINITIONDEFINE MATERIAL STARTISOTROPIC STEELE 2.05e+008POISSON 0.3DENSITY 76.8195ALPHA 1.2e-005DAMP 0.03END DEFINE MATERIALMEMBER PROPERTY AMERICAN10 12 45 TO 48 51 TO 54 TABLE ST W16X269 11 49 50 55 56 TABLE D C10X2023 24 27 28 TABLE ST W8X2421 22 25 26 TABLE ST W8X2457 TO 60 TABLE ST W10X265 TO 8 13 TO 16 65 TO 68 TABLE ST W12X3029 TO 36 TABLE ST W6X1537 TO 44 TABLE ST W6X15CONSTANTSMATERIAL STEEL ALLMEMBER RELEASE29 TO 44 START MX MY MZ29 TO 44 END MY MZSUPPORTS1 TO 4 PINNEDDEFINE MOVING LOADTYPE 1 LOAD 68.75 122.59 122.59 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 -61.05 61.05 61.05 61.05DIST 3.9 1.57 4.75 1.5 1.5 1.5 1.5 1.5 11.4 1.5 1.5 1.5 1.5 1.5 WID 2TYPE 2 LOAD 68.75 122.59 122.59 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 -61.05 61.05 61.05 61.05DIST 3.9 1.57 4.75 1.5 1.5 1.5 1.5 1.5 11.4 1.5 1.5 1.5 1.5 1.5 WID 2LOAD 1 LOADTYPE None TITLE LOAD CASE 1SELFWEIGHT Y -1LOAD GENERATION 20 ADD LOAD 1TYPE 1 -1 11 -2 ZINC 0.1LOAD GENERATION 20 ADD LOAD 2TYPE 2 2 11 -2 ZINC 0.1PERFORM ANALYSISPARAMETER 1CODE LRFDFYLD 248000 ALLTRACK 0 ALLCHECK CODE ALLPARAMETER 2CODE LRFDFIXED GROUPPARAMETER 3CODE LRFDSTEEL MEMBER TAKE OFF ALLPARAMETER 4CODE LRFDSELECT ALLPARAMETER 5CODE LRFD Page 1 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAO
ARIEL C. GUEVARRA, MENG-STRUCTURL
SELECT OPTIMIZEDSTART FOOTING DESIGNCODE AMERICANBC 120 JOINT 1 TO 4CLEAR 0.075 JOINT 1 TO 4DEPTH 0.35 JOINT 1 TO 4EMBEDMENT 0 JOINT 1 TO 4FC 21000 JOINT 1 TO 4FY 275000 JOINT 1 TO 4REINF 0.016 JOINT 1 TO 4TRACK 2 JOINT 1 TO 4DESIGN FOOTING 2END FOOTING DESIGNLOAD LIST 1DRAW ISOMSECTION 0 1 ALLPRINT SUPPORT REACTION LIST 1 TO 4FINISH
Page 2 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
STAAD.PRO CODE CHECKING - (LRFD 3RD EDITION) ********************************************
ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION =======================================================================
5 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.095 22 130.63 C 1.15 0.73 1.00 6 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.282 22 315.44 C -0.32 -0.08 1.00 7 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.269 41 288.08 C 0.74 0.07 1.00 8 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.092 41 88.39 C -1.63 0.98 1.00 9 D C10X20 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.192 21 2.62 T 0.00 -24.51 1.00 10 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.936 22 19.75 T 0.53 142.18 0.00 11 D C10X20 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.354 15 8.34 T 0.00 -44.99 1.00 12 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.337 41 2.85 T -0.75 46.81 0.00 13 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.083 2 79.02 C -0.12 0.11 0.00 14 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.473 22 230.34 C 0.12 1.77 5.00 15 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.444 41 213.99 C 0.07 2.40 5.00 16 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.100 15 72.76 C -0.04 -3.05 5.00 21 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.029 41 29.33 T 0.36 0.29 2.00 22 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.034 15 28.54 T 0.03 1.60 0.00
Page 3 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION =======================================================================
23 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.025 41 13.77 T 0.27 0.66 0.00 24 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.049 41 51.50 T -0.12 1.41 4.80 25 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.036 41 15.37 T 0.52 0.96 2.00 26 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.033 41 18.12 T 0.49 0.70 2.00 27 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.041 41 5.69 T -0.49 1.59 4.80 28 ST W8X24 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.053 41 24.22 T 0.52 1.67 0.00 29 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.250 41 26.16 C 0.00 -0.91 3.47 30 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.581 22 66.44 C 0.00 -0.91 3.47 31 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.336 22 36.57 C 0.00 -0.91 3.47 32 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.350 41 38.30 C 0.00 -0.91 3.47 33 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.093 21 13.08 C 0.00 -0.91 3.47 34 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.128 2 21.56 C 0.00 -0.91 3.47 35 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.090 21 12.36 C 0.00 -0.91 3.47 36 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.090 21 12.31 C 0.00 -0.91 3.47 37 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.253 22 49.17 C 0.00 -0.29 3.14
Page 4 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION =======================================================================
38 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.237 22 45.96 C 0.00 -0.29 3.14 39 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.317 22 62.03 C 0.00 -0.29 3.14 40 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.309 22 60.37 C 0.00 -0.29 3.14 41 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.280 35 54.68 C 0.00 -0.29 3.14 42 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.299 39 58.45 C 0.00 -0.29 3.14 43 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.252 41 49.00 C 0.00 -0.29 3.14 44 ST W6X15 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.267 41 51.98 C 0.00 -0.29 3.14 45 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.309 41 5.49 T 0.10 44.83 0.00 46 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.931 22 15.18 T -0.16 136.44 0.00 47 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.960 23 26.36 C 0.08 139.90 0.00 48 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.313 39 8.04 C 0.12 44.87 0.00 49 D C10X20 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.270 2 0.11 C 0.13 -33.78 1.00 50 D C10X20 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.006 22 0.01 T 0.07 0.37 2.00 51 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.989 27 17.74 T 0.00 -155.05 0.80 52 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.954 22 18.31 T -0.42 146.01 1.60
Page 5 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
ALL UNITS ARE - KN METE (UNLESS OTHERWISE NOTED)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION =======================================================================
53 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.342 41 4.03 T -0.66 -48.34 0.00 54 ST W16X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.339 41 5.22 T 0.79 46.66 1.60 55 D C10X20 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.391 22 0.06 T 0.01 -50.09 1.00 56 D C10X20 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.490 32 0.01 T -0.01 -62.72 1.00 57 ST W10X26 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.194 22 35.39 C 0.97 7.73 0.00 58 ST W10X26 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.092 22 12.51 C -0.92 2.90 0.00 59 ST W10X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.134 22 76.45 T -0.40 6.55 0.00 60 ST W10X26 (AISC SECTIONS) PASS LRFD-H1-1B-T 0.060 22 24.36 T -0.42 2.55 0.00 65 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.118 21 30.28 C 0.49 8.44 5.00 66 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.519 22 183.67 C 5.72 0.92 5.00 67 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1A-C 0.603 31 225.06 C -5.65 -1.41 5.00 68 ST W12X30 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.253 15 79.01 C -1.39 15.45 5.00
************** END OF TABULATED RESULT OF DESIGN **************
STEEL TAKE-OFF --------------
ST W12X30 44.00 19.168 D C10X20 12.00 6.994 ST W16X26 17.60 6.699 ST W8X24 27.20 9.544 ST W6X15 98.53 21.633 ST W10X26 21.54 8.124 ---------------- TOTAL = 72.162
PROFILE LENGTH(METE) WEIGHT(KN )
Page 6 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
FOOTING AT SUPPORT: 2 ------------------------------------------------------- UNIT : KN METR LOAD : VERTICAL LOAD = P = 346.1826 MOMENT IN X-DIR.= Hx x d + Mz = 0.0000 MOMENT IN Z-DIR.= Hz x d + Mx = 0.0000 DIMENSIONS : COLUMN SIZE = cx x cz = 0.100 x 0.150 FOOTING AREA REQUIRED = 2.89 SLAB SIZE = s1 x s2 = 1.699 x 1.699 DEPTH OF SLAB = sy = 0.350 EMBEDMENT DEPTH = 0.000 SOIL : BEARING CAPACITY = 119.918 MAXIMUM BEARING PRESSURE = 119.918
REINFORCEMENT : BOTTOM REINFORCEMENT: UNIT : MM BAR DIA. OF SLAB REINFORCEMENT (MMS) = 16 REINFORCEMENT RATIO (X-DIR) = 0.00502 REINFORCEMENT RATIO (Z-DIR) = 0.00502 AREA OF STEEL REQD. IN X-DIR = 2222.71 NO. OF BARS IN X-DIR. = 14 SPACING OF BARS IN X-DIR. = 117.00 AREA OF STEEL REQD. IN Z-DIR = 2222.71 NO. OF BARS IN Z-DIR. = 14 SPACING OF BARS IN Z-DIR. = 117.00 DOWEL REINF. : BAR # 6 REQD. AREA= 883.5 NO. OF BARS PROVIDED= 4 DEV.LENGTH= 239.3
Page 7 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
FOOTING W/O PEDESTAL : |_> 0.10 MET |_____| |__-__| | | | | | | | | | | | | | | | | |________________- _________________|_ _ _| | | 0.35 MET ________________________________________-_ _ __ |_____________ 1.70MET_____________| ELEVATION --------- ======================================================================== |_______________________________________|_ _ _ _ _ _ _ _ _ _ _ _ _ | | | | | | | | | | | | | | |<|<|<_|__ 14-#16 @ 0.12 MET | | | | | | | | | | | | | | | | | | | | | | | | | | |_____|_ _ __ __|_|_|__|_ _| 1.70MET | | | | | | | | | | | | | | | 0.15 MET | | ______-_ _ __ __|_|_|__|_ __ | | | | | | | | | | | | | | | | | | | | | |_|_|_ |__ 14-#16 @ 0.12 MET | | _______________________________|_|_|_ | | | _______________________________|_|_|_ | | | _______________________________|_|_|_ | | ________________________________________-_ _ _ _ _ _ _ _ _ _ _ _ _ _ PLAN ---- **** DESIGN SKETCHES ****
*****************END OF FOOTING DESIGN RESULTS*******************
Page 8 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
DRAW ISOM
TIME: 10:29:45
DATE:JUL 19,2015
S T A A D -III
REV: 2006
STRUCTURE DATA:
TYPE = SPACE
NJ = 24
NM = 56
NE = 0
NS = 4
NL = 41
XMAX= 2.0
YMAX= 11.0
ZMAX= 8.8
UNIT METE KN
Page 9 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
SUPPORT REACTIONS -UNIT KN METE STRUCTURE TYPE = SPACE -----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 0.03 11.36 0.10 0.00 0.00 0.00 2 1 -0.03 12.77 0.08 0.00 0.00 0.00 3 1 -0.03 12.53 -0.08 0.00 0.00 0.00 4 1 0.03 11.25 -0.10 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
104. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= JUL 19,2015 TIME= 10:29:46 ****
Page 10 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
DRAW ISOM
TIME: 21:30:24DATE:JUL 18,2015
S T A A D -IIIREV: 2006
STRUCTURE DATA:
TYPE = SPACENJ = 24NM = 56NE = 0NS = 4NL = 100
XMAX= 2.0YMAX= 11.0ZMAX= 8.8
UNIT METE KN
R1R1
R1R1
R1
R1R1
R1R1
R1
R2
R2R2
R2R2
R2
R3R3
R3R3
R4
R4
R4
R4
R5R5
R5R5
R6 R6
R6
R6
R6R6
R6R6
R6R6
Page 11 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
3D Rendered View
5.00m
5.00m
1.00m
2.00m
4.80mLoad 1
XY
Z
Whole Structure
R6R4R6
R6R8R8
R3
R6
R3
R4
R5
R7R7
R6
R6R5
R7R7
R2
R4
R8R8
R6
R1
R3
R6
R6
R1
R3
R8R8
R2
R7R7
R1
R6
R7R7
R1
R4
R2 R1
R6
R1
R8R8
R2 R1
R5R6
R1
R5
R2 R1R1 R2
Load 1X
Y
Z
Whole Structure
4.80m
2.00m
Page 12 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
STEEL COLUMN BASE PLATE ANALYSIS
Job Name: BRIDGE SUPPORT BASE PLATE DESIGN Subject:Job Number: Originator: Checker:
Input Data:
Column Size: Column Properties:Select: W12x30 A = 8.79 in.^2
Column Loadings: d = 12.300 in.Axial Load, P(total) = -70.75 kips tw = 0.260 in.Axial Load, P(DL) = 0.00 kips bf = 6.520 in.
Shear Load, V(total) = -0.06 kips tf = 0.440 in.Moment @ Base, M = 0.00 ft.-kips
Design Parameters:Base Plate Length, N = 16.000 in. ED1=1.5Base Plate Width, B = 10.000 in.
Plate Yield Stress, Fy = 36.00 ksi ED2=1.5 n=2.39Concrete Strength, f 'c = 3.000 ksi.
Bearing Area, A2 = 1296.00 in.^2Shear Coef., C = 1.85 B=10 0.80*bf
Coef. of Friction, µ = 0.55Anchor Bolt/Rod Data:
Total No. of Bolts, Nb = 6 n=2.39Bolt Diameter, db = 1.000 in.
Anchor Bolt Material = A36 m=2.16 0.95*d m=2.16Bolt Edge Dist., ED1 = 1.500 in.Bolt Edge Dist., ED2 = 1.500 in. N=16
Results: Plan
Eccentricity, Bearing Length, and Bearing Pressures: e = M*12/P = 0Eccentricity, e = 0.000 in.
Length, Xc = 16.000 in. P(total) =Fp = 2.100 ksi -70.75
fp(max) = 0.442 ksi (-down)fp(min) = 0.442 ksi
Fp >= fp(max), O.K. W12x30 Col.Anchor Bolt/Rod Tension and Shear:
Ft = 19.10 ksiTa = 15.00 k/bolt tp=0.53Tb = 0.00 k/bolt
fp(max)=0.442Fv = 9.90 ksi T= Xc=16Va = 7.78 k/bolt Tb*(Nb/2)
V(bolts) = 0.06 = V(total)-1/2*µ*P(DL) N=16Vb = 0.01 k/bolt
Va >= Vb, O.K. Elevation(Interaction) S.R. = N.A. = Tb/Ta+(C*Vb)/Va
Base Plate Thickness: Suggested plate thickness for rigidity:
be
Per AISC 9th Edition Manual (ASD) and "Design of Welded Structures" For Axial Load with or without Moment
tp(req'd) = 16.00 mm tp(min) = 16.00 mm tp(min) >= max. of m/4 or n/4
Page 13 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL
Page 14 of 14STRUCTURAL ANALYSIS AND DESIGN OF BRIDGE SUPPORT LOCATED AT LENGUA & NANGAYANGAN TUGUEGARAOARIEL C. GUEVARRA, MENG-STRUCTURL