CONTINUOUS BEAM ANALYSIS - QBASIC / FREEBASIC - STRUCTURAL ANALYSIS / CIVIL ENGINEERING

REM SHEAR AND MOMENT ENVELOPES FOR A CONTINUOUS BEAM

REM ************************************************

DIM VS(10, 11), VE(10, 11), MS(10, 21), MN(10, 21), MP(10, 21)

DIM Length(20),MomentArea(20),NumberOfLoads(20),LoadWeight(20,20)

DIM LoadStart(20,20),LoadCover(20,20),DeadOrImposedLoad$(20,20)

DIM CantileverLeft(20),CantileverRight(20),MM(20),SM(20),K2(20)

DIM DVar(20),E(20),FLeft(20),FRight(20),WD(20,20),FVar(20),R(200)

DIM ML(200),MR(200)

REM *************************************** Input of data

PRINT "ENTER TITLE"

INPUT T$

REM *************************** Partial factors of safety

PRINT "ENTER PARTIAL FACTOR OF SAFETY FOR DEAD LOAD,GK"

INPUT GK

PRINT "ENTER PARTIAL FACTOR OF SAFETY FOR IMPOSED LOAD,QK"

INPUT QK

REM *********************************** Beam information

PRINT "ENTER NO. OF SPANS"

INPUT NumberOfSpan

FOR I = 1 TO NumberOfSpan

PRINT "SPAN NO"; I

PRINT "ENTER SPAN LENGTH-metres"

INPUT Length(I)

PRINT "ENTER '2ND MOMENT OF AREA OF SPAN'S SECTION,IZ-mm^4"

INPUT MomentArea(I)

NEXT I

REM ***************** Characteristic loading information

FOR I = 1 TO NumberOfSpan

PRINT "SPAN NO."; I

PRINT "ENTER NO. OF LOADS ON SPAN"; I

INPUT NumberOfLoads(I)

IF NumberOfLoads(I) = 0 THEN 390

FOR J = 1 TO NumberOfLoads(I)

PRINT "SPAN NO. "; I; "LOAD NO. "; J

PRINT "ENTER LOAD'S CHARACTERISTIC WEIGHT-kN"

INPUT LoadWeight(I, J)

PRINT "ENTER LOAD START DISTANCE,A-metres "

INPUT LoadStart(I, J)

PRINT "ENTER LOAD COVER DISTANCE,C-metres"

INPUT LoadCover(I, J)

PRINT "ENTER LOAD DEAD OR IMPOSED - D OR I"

INPUT DeadOrImposedLoad$(I, J)

NEXT J

390 NEXT I

REM ***************** Cantilevers characteristic moments

PRINT "ENTER CANTILEVER CHARACTERISTIC DEAD MOMENT AT L.H.S.-kN.m"

INPUT CantileverLeft(1)

PRINT "ENTER CANTILEVER CHARACTERISTIC IMPOSED MOMENT AT L.H.S.-

kN.m"

INPUT CantileverLeft(2)

PRINT "ENTER CANTILEVER CHARACTERISTIC DEAD MOMENT AT R.H.S.-kN.m"

INPUT CantileverRight(1)

PRINT "ENTER CANTILEVER CHARACTERISTIC IMPOSED MOMENT AT R.H.S.-

kN.m"

INPUT CantileverRight(2)

REM ***************************** Initialising variables

CL = 0: CR = 0

FOR I = 1 TO NumberOfSpan

MM(I) = 0: SM(I) = 0

FOR K = 1 TO 21

VE(I, (K + 1) / 2) = 0: MN(I, K) = 10 ^ 10: MP(I, K) = -(10 ^ 10)

NEXT K

NEXT I

REM ************************************* Beam stiffness

FOR I = 1 TO NumberOfSpan

K2(I) = MomentArea(I) / Length(I)

NEXT I

GOSUB 4000: REM ******* Subroutine for slope deflection equations -- L.H.S

REM No. of load patterns = NP

NP = NumberOfSpan + 1

IF CantileverLeft(1) + CantileverLeft(2) > 0 THEN NP = NP + 1

IF CantileverRight(1) + CantileverRight(2) > 0 THEN NP = NP + 1

REM ********************* Analysis for each load pattern

LP = 0

680 LP = LP + 1

GOSUB 9000: REM ***Subroutine to calculate design loads

GOSUB 5000: REM ****** Subroutine for fixed end moments

GOSUB 6000: REM ******* Subroutine for slope deflection equations - R.H.S.

GOSUB 7000: REM Subroutine for sol'n of eq'ons and c'tion of end moments

GOSUB 8000: REM Subroutine for span shear and moments

GOSUB 10000: REM Subroutine to sort for shear and moment envelopes

IF LP < NP THEN 680 REM *** Sort for maximum sagging moment and its

position FOR I = 1 TO NumberOfSpan FOR K = 1 TO 21 IF MP(I, K) > MM(I)

THEN MM(I) = MP(I, K): SM(I) = Length(I) * (K - 1) / 20

NEXT K

NEXT I

REM *********************** Printout of data and results

OPEN "BEAMOUT.TXT" FOR OUTPUT AS #1

PRINT #1, "TITLE "

PRINT #1, "PARTIAL FACTORS OF SAFETY"

PRINT #1, "FACTOR OF SAFETY FOR DEAD LOAD ="; GK

PRINT #1, "FACTOR OF SAFETY FOR DEAD LOAD ="; GK

PRINT #1, "FACTOR OF SAFETY FOR IMPOSED LOAD="; QK

PRINT #1,

PRINT #1, : PRINT #1, "STRUCTURE INFORMATION"

PRINT #1, "---------------------"

PRINT #1, "NO. OF SPANS "; NumberOfSpan

PRINT #1,

PRINT #1, " SPAN SPAN 2ND MOMENT"

PRINT #1, " NO. LENGTH(m) OF AREA(mm^4)"

FOR I = 1 TO NumberOfSpan

PRINT #1, USING " ## ####.## ####.##"; I; Length(I); MomentArea(I)

NEXT I

REM

PRINT #1, : PRINT #1, : PRINT #1, "LOADING INFORMATION"

PRINT #1, "-------------------"

PRINT #1, " SPAN LOAD START COVER DEAD "

PRINT #1, " NO. WEIGHT(kN) DISTANCE(m) DISTANCE(m) OR IMPOSED"

FOR I = 1 TO NumberOfSpan

IF NumberOfLoads(I) = 0 THEN 1080

FOR J = 1 TO NumberOfLoads(I)

PRINT #1, USING " ## ####.## ####.## ####.## \ \"; I; LoadWeight(I, J);

LoadStart(I, J); LoadCover(I, J); DeadOrImposedLoad$(I, J)

NEXT J

1080 NEXT I

REM

PRINT #1, "CANTILEVER CHARACTERISTIC DEAD MOMENT AT L.H.S.=";

CantileverLeft(1); "kN.m"

PRINT #1, "CANTILEVER CHARACTERISTIC IMPOSED MOMENT AT L.H.S.=";

CantileverLeft(2); "kN.m"

PRINT #1, "CANTILEVER CHARACTERISTIC DEAD MOMENT AT R.H.S.=";

CantileverRight(1); "kN.m"

PRINT #1, "CANTILEVER CHARACTERISTIC IMPOSED MOMENT AT R.H.S.=";

CantileverRight(2); "kN.m"

REM ******************************* Printout of results

PRINT "PRINT RESULT IN BEAMOUT.TXT FILE"

PRINT #1, : PRINT #1, : PRINT #1, "SHEAR AND MOMENT ENVELOPES"

PRINT #1, "__________________________"

PRINT #1, "SHEARS,kN AND MOMENTS,kN.m AT 10TH INTERVALS ALONG

SPANS"

FOR I = 1 TO NumberOfSpan

PRINT #1, : PRINT #1, "SPAN NO."; I

PRINT #1, "SECTION SHEAR HOGGING SAGGING"

PRINT #1, " NO. MOMENT MOMENT"

FOR K = 1 TO 21 STEP 2

PRINT #1, USING " ## ####.## ####.## ####.##"; (K + 1) / 2; VE(I, (K + 1) /

2); MN(I, K); MP(I, K)

REM

NEXT K

PRINT #1, "MAXIMUM SPAN MOMENT = "; INT(MM(I) * 100) / 100; "kN.m"

PRINT #1, "AT A DISTANCE = "; INT(SM(I) * 100) / 100; "metres"

NEXT I

CLOSE #1

END

REM ***************************************************

4000 REM Subroutine for slope deflection equations - L.H.S.

DVar(1) = 4 * K2(1): E(1) = 2 * K2(1)

FOR I = 2 TO NumberOfSpan

DVar(I) = 4 * (K2(I - 1) + K2(I))

E(I) = 2 * K2(I)

NEXT I

DVar(NumberOfSpan + 1) = 4 * K2(NumberOfSpan)

E(NumberOfSpan + 1) = 0

RETURN

REM ***************************************************

5000 REM ********* Subroutine to calculate fixed end moments

FOR I = 1 TO NumberOfSpan

FLeft(I) = 0: FRight(I) = 0

IF NumberOfLoads(I) = 0 THEN 5120

FOR J = 1 TO NumberOfLoads(I)

W = WD(I, J): A = LoadStart(I, J): C = LoadCover(I, J): L = Length(I)

S = A + C / 2: T = L - S

FL = W * (S * T ^ 2 + (S - 2 * T) * C ^ 2 / 12) / L ^ 2

FR = W * (T * S ^ 2 + (T - 2 * S) * C ^ 2 / 12) / L ^ 2

FLeft(I) = FLeft(I) + FL

FRight(I) = FRight(I) + FR

NEXT J

5120 NEXT I

RETURN

REM ***************************************************

6000 REM Subroutine for slope deflection equations - R.H.S.

FVar(1) = -(FLeft(1)) + CL

FOR I = 2 TO NumberOfSpan

FVar(I) = FRight(I - 1) - FLeft(I)

NEXT I

FVar(NumberOfSpan + 1) = FRight(NumberOfSpan) - CR

RETURN

REM ***************************************************

7000 REM *** Subroutine for equation solution and end moment calculation

D = DVar(1): F = FVar(1)

FOR I = 2 TO NumberOfSpan + 1

F = FVar(I) - E(I - 1) * F / D

D = DVar(I) - E(I - 1) ^ 2 / D

NEXT I

R(NumberOfSpan + 1) = F / D

R(NumberOfSpan) = (FVar(NumberOfSpan + 1) - DVar(NumberOfSpan + 1) *

R(NumberOfSpan + 1)) / E(NumberOfSpan)

FOR I = NumberOfSpan TO 2 STEP -1

R(I - 1) = (FVar(I) - DVar(I) * R(I) - E(I) * R(I + 1)) / E(I - 1)

NEXT I

REM End moments

FOR I = 1 TO NumberOfSpan

ML(I) = (4 * R(I) + 2 * R(I + 1)) * K2(I) + FLeft(I)

MR(I) = (2 * R(I) + 4 * R(I + 1)) * K2(I) - FRight(I)

NEXT I

RETURN

REM ***************************************************

8000 REM *** Subroutine to calculate span shears and moments

FOR I = 1 TO NumberOfSpan

REM ***** Calculation of span shears and moments due to end moments

RL = (ML(I) + MR(I)) / Length(I)

FOR K = 1 TO 11: VS(I, K) = RL: NEXT K

FOR K = 1 TO 21: MS(I, K) = -ML(I) + RL * Length(I) * (K - 1) / 20: NEXT K

FOR J = 1 TO NumberOfLoads(I)

IF NumberOfLoads(I) = 0 THEN 8300

W = WD(I, J): A = LoadStart(I, J): C = LoadCover(I, J): L = Length(I)

S = L - A - C / 2

RL = W * S / L: RR = W - RL

REM ********************* Span shears at 10th intervals

FOR K = 1 TO 11

Z = (K - 1) * L / 10

IF Z <= A THEN VK = RL: GOTO 8180 IF Z > A + C THEN VK = -RR: GOTO 8180

Z1 = Z - A

VK = RL - W * Z1 / C

8180 VS(I, K) = VS(I, K) + VK

NEXT K

REM ******************** Span moments at 20th intervals

FOR K = 1 TO 21

Z = (K - 1) * L / 20

IF Z <= A THEN MK = RL * Z: GOTO 8270 IF Z >= A + C THEN MK = RR * (L - Z):

GOTO 8270

Z1 = Z - A: WZ = W * Z1 / C

MK = RL * Z - WZ * Z1 / 2

8270 MS(I, K) = MS(I, K) + MK

NEXT K

NEXT J

8300 NEXT I

RETURN

REM ***************************************************

9000 REM ************** Subroutine to calculate design loads

FOR I = 1 TO NumberOfSpan

IF NumberOfLoads(I) = 0 THEN 9290

REM **************************** Partial safety factors

GG = 1: QG = 0

IF LP = 1 THEN 9090

IF LP = 2 THEN 9120

IF LP > 2 AND LP < NumberOfSpan + 2 THEN 9150

IF LP > NumberOfSpan + 1 THEN 9190

9090 REM ******* Odd numbered spans, maximum sagging moments

IF I / 2 > INT(I / 2) THEN 9230

GOTO 9240

9120 REM ****** Even numbered spans, maximum sagging moments

IF I / 2 = INT(I / 2) THEN 9230

GOTO 9240

9150 REM *************************** Maximum support moments

IF I = LP - 2 THEN 9230

IF I = LP - 1 THEN 9230

GOTO 9240

9190 REM **** Maximum shear at end supports with cantilevers

IF LP = NumberOfSpan + 2 AND I = 1 THEN 9230

IF LP = NumberOfSpan + 3 AND I = NumberOfSpan THEN 9230

GOTO 9240

9230 GG = GK: QG = QK

9240 REM ************************************** Design loads

FOR J = 1 TO NumberOfLoads(I)

IF UCASE$(DeadOrImposedLoad$(I, J)) = "D" THEN WD(I, J) = LoadWeight(I, J)

* GG

IF UCASE$(DeadOrImposedLoad$(I, J)) = "I" THEN WD(I, J) = LoadWeight(I, J)

* QG

NEXT J

9290 NEXT I

REM ************************* Cantilever design moments

IF CantileverLeft(1) + CantileverLeft(2) = 0 THEN 9370

GG = 1: QG = 0

REM *********************************** Left cantilever

IF LP = 2 THEN GG = GK: QG = QK

IF LP = NumberOfSpan + 2 THEN GG = GK: QG = QK

CL = CantileverLeft(1) * GG + CantileverLeft(2) * QG

9370 REM ********************************** Right cantilever

IF CantileverRight(1) + CantileverRight(2) = 0 THEN 9440

GG = 1: QG = 0

IF LP = 1 AND NumberOfSpan / 2 = INT(NumberOfSpan / 2) THEN GG = GK:

QG = QK

IF LP = 2 AND NumberOfSpan / 2 > INT(NumberOfSpan / 2) THEN GG = GK:

QG = QK

IF LP = NumberOfSpan + 3 THEN GG = GK: QG = QK

CR = CantileverRight(1) * GG + CantileverRight(2) * QG

9440 RETURN

REM ***************************************************

10000 REM *** Subroutine to sort for shear force and bending moment

envelopes

REM *********************************** Shear envelope

FOR I = 1 TO NumberOfSpan

FOR K = 1 TO 11

IF ABS(VE(I, K)) < ABS(VS(I, K)) THEN VE(I, K) = VS(I, K)

NEXT K

NEXT I

REM ************************** Bending moment envelope

FOR I = 1 TO NumberOfSpan

FOR K = 1 TO 21

REM ********************************* Hogging envelope

IF MN(I, K) > MS(I, K) THEN MN(I, K) = MS(I, K)

IF MN(I, K) > 0 THEN MN(I, K) = 0

REM ********************************* Sagging envelope

IF MP(I, K) < MS(I, K) THEN MP(I, K) = MS(I, K)

IF MP(I, K) < 0 THEN MP(I, K) = 0

NEXT K

NEXT I

RETURN

REM **************************************************