f35a0b71-1bbe-41ad-9bd8-17c4189cc13d 662 NDTM Amarasekera 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Note: Definitions in "Include Programs.sm" is highlighted in light blue

4 appVersion 1.0.8348.30405

Includes the definitions from an external SMath file Include_Programs-R10.sm include 43

4 - appVersion 1.0.8348.30405 ≡

Define kNm kN m * :

Assume E 1 MPa * :

Assume Young's Modulus for RC: This is not really required, but used only for consistent units in intermediate calculations. We can use any numerical value. Ex E = 1 MPa

t.0 0 time :

Example 13.1 Simplified analysis of concrete framed building—vertical load
(a) Specification
The cross-section of a reinforced concrete building is shown in Fig. 13.5(a). The frames are at 4.5 m centres, the length of the building is 36 m and the column bases are fixed. Preliminary sections for the beams and columns are shown in Fig. 13.5(b). The floor and roof slabs are designed to span one way between the frames. Longitudinal beams are provided between external columns of the roof and floor levels only. :

Member Stiffness (ST)
cond = 0.75 when Pinned at base.
cond = 1 when fixed at both ends.
This program can handle both cases as shown below.

cond Pinned 0.75 Fixed 122 mat :

"Pinned"
"Fixed"

FDN

DATA

3 upper columns, 3 lower columns and 2 beams

FDN 1

Column b.UC 30030030031 mat mm * : h.UC 40040040031 mat mm * : b.LC 40040040031 mat mm * : h.LC 50050050031 mat mm * : H.UC 4.0 4.0 4.0 31 mat m * : H.LC 5.5 5.5 5.5 31 mat m * : 61 line

Beam b.beam 40040021 mat mm * : h.beam 60060021 mat mm * : L 6821 mat m * : 31 line

Define kNm kN m * :

Assume E 1 MPa * :

Flanged Beams can be effective only in case of sagging as the concrete is able to take compression. In limit state design we neglect the tensile strength of concrete. As a result, at supports, continuous 'T' beams should be designed as a rectangular beam (with width equal to the web width).

Defie Line.zero 00 L m / (sum 022 mat :

Define LL 1 L rows range el 0 : 0021 mat

Moment of Inertia

Upper Columna I.UC 112 / b.UC * h.UC (3^* vectorize : mm 4^1.6 109^* 1.6 109^* 1.6 109^* 31 mat

Lower Columna I.LC 112 / b.LC * h.LC (3^* vectorize : mm 4^4.1667 109^* 4.1667 109^* 4.1667 109^* 31 mat

Beams I.beam 112 / b.beam * h.beam (3^* vectorize : mm 4^7.2 109^* 7.2 109^* 21 mat

Foundation Columns Fixed at Base blue light green 1 3 mat FDN 1 ≡ Foundation Columns Pinned at Base black pink 1 3 mat FDN 0.75 ≡ Wrong Input : Pl check Red pink 1 3 mat cases Foundation Columns Fixed at Base blue light green 1 3 mat FDN 1 ≡ Foundation Columns Pinned at Base black pink 1 3 mat FDN 0.75 ≡ Wrong Input : Pl check Red pink 1 3 mat cases

FDN 1

Call Program 2 to find the Stiffness Matrix of the Sustitute Frame K1 L I.UC I.LC I.beam H.UC H.LC FDN Find_K : kNm 9.4303 2.4 0 2.4 13.0303 1.8 0 1.8 8.2303 33 mat

Frames are spaced at 5 m

Loadings

S.frame 4.5 m * : L.building 36 m * : γ.cu 24 kN m 3^/ * : 31 line

finishes.floor 0.5 kN m 2^/ * : q.k_floor 4.0 kN m 2^/ * : 21 line

slab.thick 175 mm * :

2A. Self weights, Dead loads

Self Weight of Beam W.beam h.beam 1 el slab.thick - (b.beam 1 el * γ.cu * : kN m / 4.08

D/L from Slab W.slab slab.thick γ.cu * finishes.floor + : kN m 2^/ 4.7

Floors D/L g.k_floor 6.2 kN m 2^/ * :

Floors I/L q.k_floor 3.0 kN m 2^/ * :

2B. Design Loads on Beams

Dead load

Imposed loadd

G.k_floor g.k_floor S.frame * : kN m / 27.9

Q.k_floor q.k_floor S.frame * : kN m / 13.5

Max Design Load

Min Design Load

F1 1.4 G.k_floor * 1.6 Q.k_floor * + : kN m / 60.66

F2 1.0 G.k_floor * : kN m / 27.9

Define Load Patterns for All 4 Cases

Case I

Case II

Case III

FF F1 F1 21 mat F1 F2 21 mat F2 F1 21 mat 13 mat : kN m / 60.66 60.66 21 mat 60.66 27.9 21 mat 27.9 60.66 21 mat 13 mat

3 load cases have been considered in this example

Call Program 7 to find support moments, upper & lower column moments M.all FF K1 H.UC H.LC I.beam I.UC I.LC FDN L NEW_BMM :

FDN 1

Upper
Col

Lower
Col

M.all kNm 73.1 - 286.1 12 mat 350 - 19612 mat 25.3 22.1 67.7 - 31 mat 47.8 41.8 128.3 - 31 mat 94 - 211.9 12 mat 193.9 - 79.8 12 mat 32.5 6.2 - 27.6 - 31 mat 61.5 11.8 - 52.2 - 31 mat 12.8 - 205.8 12 mat 317.1 - 206.4 12 mat 4.4 38.5 71.3 - 31 mat 8.3 72.9 135.1 - 31 mat 34 mat

Foundation Columns Fixed at Base blue light green 1 3 mat FDN 1 ≡ Foundation Columns Pinned at Base black pink 1 3 mat FDN 0.75 ≡ Wrong Input : Pl check Red pink 1 3 mat cases

Results using Moment Distribution Program - With 7 iterations

Get Column Moments

M.col M.all 1 M.all rows range M.all cols 1 - (M.all cols range el :

Call Program 9 : Sum of Upper & Lower Col Moments Col_Sum M.col Sum_Col_M : kNm 73.09 63.91 195.99 31 mat 93.95 18.08 79.76 31 mat 12.75 111.38 206.37 31 mat 31 mat

M.col kNm 25.26 22.08 67.72 - 31 mat 47.83 41.82 128.26 - 31 mat 32.47 6.25 - 27.56 - 31 mat 61.49 11.83 - 52.2 - 31 mat 4.41 38.49 71.31 - 31 mat 8.34 72.89 135.06 - 31 mat 32 mat

Case I

Case II

Case III

Beam1

Center Beam

M.sup M.all 1 M.all rows range 1 L rows range el : kNm 73.1 - 286.1 12 mat 350 - 19612 mat 94 - 211.9 12 mat 193.9 - 79.8 12 mat 12.8 - 205.8 12 mat 317.1 - 206.4 12 mat 32 mat

Case I Case II Case III

Convert the nested matrix to its absolute values MM.sup M.sup abs vectorize vectorize vectorize : kNm 7328612 mat 35019612 mat 9421212 mat 1948012 mat 1320612 mat 31720612 mat 32 mat

SF1
kN

SF2
kN

Max Span M
kNm

X_Max
m

Call PROGRAMS 11 : Find SF, Max Span BM & X_max for ALL Loading Cases Res_All M.all FF L Find_All : 1.46 105^* kg m * s 2^/ * 2.62 105^* kg m * s 2^/ * 21 mat 2.17 105^* kg m * s 2^/ * - 2.23 105^* kg m * s 2^/ * - 21 mat 1.04 105^* kg m 2^* s 2^/ * - 2.15 105^* kg m 2^* s 2^/ * - 21 mat 2.41 m * 4.32 m * 21 mat 14 mat 1.62 105^* kg m * s 2^/ * 1.26 105^* kg m * s 2^/ * 21 mat 2.02 105^* kg m * s 2^/ * - 97337.37 kg m * s 2^/ * - 21 mat 1.23 105^* kg m 2^* s 2^/ * - 90034.95 kg m 2^* s 2^/ * - 21 mat 2.68 m * 4.51 m * 21 mat 14 mat 51530.18 kg m * s 2^/ * 2.56 105^* kg m * s 2^/ * 21 mat 1.16 105^* kg m * s 2^/ * - 2.29 105^* kg m * s 2^/ * - 21 mat 34835.95 kg m 2^* s 2^/ * - 2.25 105^* kg m 2^* s 2^/ * - 21 mat 1.85 m * 4.23 m * 21 mat 14 mat 31 mat

Case 1

Case 2

Case 3

Note: MATRIX VECTORIZE & TRANSPOSE . Extensively used to transform display of some outputs

CALL PROGRAM 12 : Extract All SFF SFF Res_All Calc_SF : kN 146.5 261.9 21 mat 217.5 - 223.4 - 21 mat 162.3 125.9 21 mat 201.6 - 97.3 - 21 mat 51.5 256.5 21 mat 115.9 - 228.8 - 21 mat 32 mat

Convert SFF to absolute values SFF.ABS SFF abs vectorize vectorize vectorize : kN 146.5 261.9 21 mat 217.5 223.4 21 mat 162.3 125.9 21 mat 201.6 97.3 21 mat 51.5 256.5 21 mat 115.9 228.8 21 mat 32 mat

Beam1

Beam 2

Call Program 8 SFF.max SFF.ABS Find_Max_Abs : kN 261.89

SFF vectorize transpose kN 146.5 217.5 - 162.3 201.6 - 51.5 115.9 - 32 mat 261.9 223.4 - 125.9 97.3 - 256.5 228.8 - 32 mat 12 mat

CALL PROGRAM 14 : Extract All Span Moments M.span Res_All Span_M : kNm 103.8 - 215.3 - 21 mat 123.2 - 90 - 21 mat 34.8 - 225.1 - 21 mat 31 mat

MATRIX VECTORIZE & TRANSPOSE

Beam1

Beam 2

M.span vectorize transpose kNm 103.8 - 123.2 - 34.8 - 31 mat 215.3 - 90 - 225.1 - 31 mat 12 mat

CALL PROGRAM 15 : Extract All X-max X.max Res_All X_Max : m 2.4 4.3 21 mat 2.7 4.5 21 mat 1.8 4.2 21 mat 31 mat

Case I

Case II

Case III

CALL Programs 18 : To Plot BMD for ALL Cases BMD_All M.sup SFF L FF BMD_All_Cases :

BMD_All 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6311 mat 73.1 45 19.4 3.9 - 24.7 - 43.1 - 59 - 72.5 - 83.6 - 92.3 - 98.5 - 102.4 - 103.8 - 102.7 - 99.3 - 93.4 - 85.1 - 74.3 - 61.1 - 45.6 - 27.5 - 7.1 - 15.8 41.1 68.8 99 131.5 166.5 204 243.8 286.1 311 mat 12 mat 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8411 mat 350 298.9 250.1 203.8 159.9 118.5 79.4 42.8 8.6 23.1 - 52.4 - 79.3 - 103.8 - 125.9 - 145.5 - 162.7 - 177.5 - 189.8 - 199.7 - 207.2 - 212.3 - 214.9 - 215.1 - 212.9 - 208.3 - 201.2 - 191.7 - 179.8 - 165.4 - 148.7 - 129.5 - 107.8 - 83.8 - 57.3 - 28.4 - 2.9 36.7 72.9 111.5 152.5 196411 mat 12 mat 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6311 mat 94 62.7 33.9 7.5 16.5 - 38 - 57.2 - 73.8 - 88.1 - 99.9 - 109.4 - 116.3 - 120.9 - 123 - 122.7 - 120 - 114.9 - 107.3 - 97.3 - 84.9 - 70 - 52.8 - 33 - 10.9 - 13.6 40.6 70 101.9 136.1 172.8 211.9 311 mat 12 mat 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8411 mat 193.9 169.2 145.7 123.4 102.1 81.9 62.9 45 28.2 12.5 2.1 - 15.5 - 27.9 - 39.1 - 49.2 - 58.2 - 66.1 - 72.8 - 78.5 - 83 - 86.4 - 88.7 - 89.9 - 89.9 - 88.9 - 86.7 - 83.4 - 79 - 73.5 - 66.9 - 59.1 - 50.2 - 40.3 - 29.2 - 17 - 3.6 - 10.8 26.4 43.1 60.9 79.8 411 mat 12 mat 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6311 mat 12.8 3 5.6 - 13.1 - 19.5 - 24.8 - 29 - 32 - 34 - 34.8 - 34.5 - 33.1 - 30.6 - 26.9 - 22.2 - 16.3 - 9.3 - 1.2 - 8 18.4 29.8 42.4 56.1 70.9 86.8 103.9 122 141.3 161.7 183.2 205.8 311 mat 12 mat 15 mat

CALL Program 21 : Cordinates of Max Span Moments Pts_MSpan X.max M.span L Pts_All_Cases : 2.4 103.8 - 12 mat 10.3 215.3 - 12 mat 21 mat 2.7 123.2 - 12 mat 10.5 90 - 12 mat 21 mat 1.8 34.8 - 12 mat 10.2 225.1 - 12 mat 21 mat 31 mat

X.max m 2.4 4.3 21 mat 2.7 4.5 21 mat 1.8 4.2 21 mat 31 mat

M.span kNm 103.8 - 215.3 - 21 mat 123.2 - 90 - 21 mat 34.8 - 225.1 - 21 mat 31 mat

Call Program 8 M.sup_max MM.sup Find_Max_Abs : kNm 350

Use Ceil2 function M.sup_max kNm / 50 Ceil 400

Use Ceil2 function SFF.max kN / 50 Ceil 300

Call Program 8 M_Span.max MSpan.ABS Find_Max_Abs :

MSpan.ABS M.span abs vectorize vectorize vectorize :

M_Span.max kNm 225.1017

CALL Program 23 : X cordinates to plot support moments X_Cord L Sup_Xcord : m 0661441 mat

CALL Program 24 : Get BMD Cases BMD BMD_All LL FF Find_BMD_Cases :

BMD rows 3

BMD cols 1

FF 1 el rows 2

BM_Case 1 FF cols range : 12331 mat

Y.Sup_Max M.sup_max kNm / 50 Ceil : 400

Y.Span_Min M_Span.max kNm / 400 Ceil : 400

Case Number Selected

nn 1

M_Span.max kNm / 225.1017

X Y Plot Settings

PLT XYPlot1 :

XYPlot.XLimMax 1 el L sum m / 1 + : 1511 mat

XYPlot.XLimMin 1 el 1 - :

XYPlot.YLimMin 1 el Y.Span_Min - : 400 - 11 mat

XYPlot.YLimMax 1 el Y.Sup_Max : 40011 mat

XYPlot.XTick 1 el 1 :

XYPlot.YTick 1 el 50 :

XYPlot1.XYLabel.XLabel Length (m) setprop 1

XYPlot1.XYLabel.YLabel BM (kNm) setprop 1

font pName XY.labelFont {pName}.XYLabel.LabelFont font setprop :

Pts_MSpan nn el 2.4 103.8 - 12 mat 10.3 215.3 - 12 mat 21 mat

Trebuchet MS,8pt XYPlot1 XY.labelFont 1

XYPlot1.XYLabel.LabelFontColor brown setprop 1

nn 1

MyTitle FIRST FLOOR BMD: Case nn num2str concat : FIRST FLOOR BMD: Case 1

XYPlot1.Title.Text MyTitle setprop 1

XYPlot1.Title.TitleFont Trebuchet MS,8pt setprop 1

CALL  Programs 25 : Plot BMD for a given CASE Number nn nn Plot_BMD transpose 0 73.09 0.2 45.01 0.4 19.35 0.6 3.88 - 0.8 24.68 - 1 43.06 - 1.2 59.01 - 1.4 72.53 - 1.6 83.63 - 1.8 92.3 - 2 98.54 - 2.2 102.36 - 2.4 103.75 - 2.6 102.72 - 2.8 99.26 - 3 93.37 - 3.2 85.06 - 3.4 74.31 - 3.6 61.15 - 3.8 45.55 - 4 27.54 - 4.2 7.09 - 4.4 15.78 4.6 41.08 4.8 68.81 5 98.96 5.2 131.54 5.4 166.54 5.6 203.97 5.8 243.83 6 286.11 312 mat 6 350.02 6.2 298.86 6.4 250.12 6.6 203.8 6.8 159.92 7 118.46 7.2 79.42 7.4 42.82 7.6 8.64 7.8 23.12 - 8 52.45 - 8.2 79.35 - 8.4 103.82 - 8.6 125.87 - 8.8 145.5 - 9 162.69 - 9.2 177.46 - 9.4 189.8 - 9.6 199.72 - 9.8 207.21 - 10 212.28 - 10.2 214.91 - 10.4 215.13 - 10.6 212.91 - 10.8 208.27 - 11 201.2 - 11.2 191.71 - 11.4 179.79 - 11.6 165.44 - 11.8 148.66 - 12 129.46 - 12.2 107.84 - 12.4 83.79 - 12.6 57.31 - 12.8 28.4 - 13 2.93 13.2 36.69 13.4 72.87 13.6 111.49 13.8 152.52 14 195.99 412 mat 12 mat

CALL Program 27 : Arrange Support Moment values & X cordinates Pts_MSup M.sup kNm / X_Cord m / Arrange_M_Sup_All : 0 73.1 12 mat 6 286.1 12 mat 635012 mat 1419612 mat 41 mat 09412 mat 6 211.9 12 mat 6 193.9 12 mat 14 79.8 12 mat 41 mat 0 12.8 12 mat 6 205.8 12 mat 6 317.1 12 mat 14 206.4 12 mat 41 mat 31 mat

M.sup kNm 73.1 - 286.1 12 mat 350 - 19612 mat 94 - 211.9 12 mat 193.9 - 79.8 12 mat 12.8 - 205.8 12 mat 317.1 - 206.4 12 mat 32 mat

Pts_MSup nn el 0 73.1 12 mat 6 286.1 12 mat 635012 mat 1419612 mat 41 mat

nn 1

CALL Program 28 : Labels to plot Pts_MSup nn el Plot_Labs 0 73.1 73.1 6 red 6 286.1 286.1 6 red 6350 350.0 6 red 14196 196.0 6 red 45 mat

CALL Program 28 : Labels to plot Pts_MSpan nn el Plot_Labs 2.4 103.8 - -103.8 6 red 10.3 215.3 - -215.3 6 red 25 mat

MM.sup transpose nn col kNm 7328612 mat 35019612 mat 21 mat

M.span nn el kNm 104 - 215 - 21 mat

Line.zero 0014022 mat

M.sup_max kNm 350

M_Span.max kNm 225.1

X.max nn el m 2.4 4.3 21 mat

FF nn el kN m / 60.66 60.66 21 mat

L m 6821 mat

nn Plot_BMD Pts_MSpan nn el Pts_MSpan nn el Plot_Labs Line.zero Pts_MSup nn el Plot_Labs 5 1 sys

0 time t.0 - 0.5 s *

Shear Force Diagram

CALL Program 29 : Arrange SF values to PLOT Plot_SF X_Cord SFF Arrange_SF : 0 146.5 6 217.5 - 6 261.9 14 223.4 - 42 mat 0 162.3 6 201.6 - 6 125.9 14 97.3 - 42 mat 0 51.5 6 115.9 - 6 256.5 14 228.8 - 42 mat 31 mat

SF_Case 1 FF cols range : 12331 mat

Define

nn2

CALL Program 19 L Get_L m / 0621 mat

Program 33 X.0 0012 mat

nn2 1

CALL Program 31: Labels to print SF zero x_cordinates on SFD n# Labs_ZeroSF X.max n# 1 el Find_Labs_ZeroSF :

X.L L m / (sum 0 augment : 14012 mat

nn2 Plot_SF X.0 Plot_SF nn2 el X.L stack :

nn2 Labs_ZeroSF 2.41 0 2.41 6 red 10.32 0 4.32 6 red 25 mat

nn2 Plot_SF 000 146.5 6 217.5 - 6 261.9 14 223.4 - 14062 mat

CALL Program 30 :Labels to print SF values on SFD Plot_SF nn2 el Plot_Labs_SF 0 146.48 146.5 6 black 6 217.48 - -217.5 6 black 6 261.89 261.9 6 black 14 223.39 - -223.4 6 black 45 mat

X Y Plot Settings for SFD

XYPlot.XLimMax 2 el L sum m / 2 + : 151621 mat

Y.SF_Max SFF.max kN / 100 Ceil : 300

XYPlot.XLimMin 2 el 1 - :

XYPlot.YLimMin 2 el Y.SF_Max - :

XYPlot.YLimMax 2 el Y.SF_Max :

LL 0021 mat

XYPlot.XTick 2 el 1 :

XYPlot.YTick 2 el 50 :

XYPlot2.XYLabel.XLabel Length (m) setprop 1

Line.zero 0014022 mat

XYPlot2.XYLabel.YLabel SF (kN) setprop 1

font pName XY.labelFont {pName}.XYLabel.LabelFont font setprop :

nn2 1

Trebuchet MS,8pt XYPlot2 XY.labelFont 1

XYPlot2.XYLabel.LabelFontColor brown setprop 1

MyTitle FIRST FLOOR SFD: Case nn2 num2str concat : FIRST FLOOR SFD: Case 1

XYPlot2.Title.Text MyTitle setprop 1

XYPlot2.Title.TitleFont Trebuchet MS,8pt setprop 1

SFF.max kN 261.9

nn2 Zero_SF L Get_L X.max nn2 el + m / LL augment : 2.41 0 10.32 022 mat

L Get_L m 0621 mat

X.max nn2 el m 2.41 4.32 21 mat

LL 0021 mat

nn2 Labs_ZeroSF 2.41 0 2.41 6 red 10.32 0 4.32 6 red 25 mat

nn2 Plot_SF 000 146.48 6 217.48 - 6 261.89 14 223.39 - 14062 mat

Plot_SF nn2 el Plot_Labs_SF 0 146.5 146.5 6 black 6 217.5 - -217.5 6 black 6 261.9 261.9 6 black 14 223.4 - -223.4 6 black 45 mat

Beam Shear Forces

Beam1

Beam 2

SFF vectorize transpose kN 146217 - 162202 - 52116 - 32 mat 262223 - 12697 - 256229 - 32 mat 12 mat

Case 1
Case 2
Case 3

nn2 Plot_SF Line.zero Plot_SF nn2 el Plot_Labs_SF nn2 Zero_SF nn2 Labs_ZeroSF 5 1 sys 1 Plot_BMD 2 Plot_BMD 3 Plot_BMD Line.zero Pts_MSpan 1 el Pts_MSpan 2 el Pts_MSpan 3 el 7 1 sys Plot_SF 1 el Plot_SF 2 el Plot_SF 3 el Line.zero 4 1 sys

0 time t.0 - 0.7 s *

Plotting Column Moments

Unlike BMD and SFD, plotting Column Moments is reatively difficult, The main reason is that both Column Moments and the Column locations have to be plotted on the X-axis. Hence, Column moment values are divided by total length of the horizontal beams. Then these values are converted to strings and plotted at the proper locations for both upper and lower columns.

Upper Lower

M.col kNm 25.3 22.1 67.7 - 31 mat 47.8 41.8 128.3 - 31 mat 32.5 6.2 - 27.6 - 31 mat 61.5 11.8 - 52.2 - 31 mat 4.4 38.5 71.3 - 31 mat 8.3 72.9 135.1 - 31 mat 32 mat

Col_Case 1 FF cols range : 12331 mat

Number of Columns N.cols L rows 1 + : 3

Define

nn3

nn3 1

Max.col_top M.col 1 col Max_Abs Max : kNm 71.3

Min.col_top M.col 1 col Min_Abs Min : kNm 4.4

Max.col_bot M.col 2 col Max_Abs Max : kNm 135.1

Min.col_bot M.col 2 col Min_Abs Min : kNm 8.3

Scale to plot column moments SC Max.col_top Max.col_bot / 0 round : 1

Note: In CASES 1 & 2, the column moments at joint 1 are large compared to CASE 3. Hence. the plot will looks odd, and to avoid such a situation, a SCALE is arbitrarily introduced in PLOTTING the column moments

SC 2 :

nn3 1

FDN 1

Already defined at the start

Call Program 36: To Plot Upper Column Moments MCol.top M.col 1 col L nn3 H.UC 1 SC Plot_UP_Col_M :

Call Program 37: To Plot Lower Column Moments MCol.bot M.col 2 col L nn3 H.LC 1 - FDN SC Plot_LOW_Col_M :

CALL Program 38: Convert Top Col Moments to strings MSTR.top nn3 M.col MStr2.top : 2522 -68 31 mat

CALL Program 38: Convert Bot Col Moments to strings MSTR.bot nn3 M.col MStr2.bot : 4842 -128 31 mat

Call Program 35: Stack Upper Col matrices Cords.top MCol.top 1 N.cols range el STACK : 0.9 0 6.8 0 11.6 032 mat

Call Program 35: Stack Bottom Col matrices Cords.bot MCol.bot 1 N.cols (range el STACK : 1.7 - 0 4.5 0 18.6 032 mat

Upper Column - Cordinates to plot moments

Bottom Column - Cordinates to plot moments

MCol.top 00 0.9 022 mat 60 6.8 022 mat 140 11.6 022 mat 000422 mat 606422 mat 14014422 mat 0.5 - 40422 mat 5.6 46422 mat 15.2 414422 mat 0.5 - 4 0.9 022 mat 5.6 4 6.8 022 mat 15.2 4 11.6 022 mat 121 mat

MCol.top 00 0.9 022 mat 60 6.8 022 mat 140 11.6 022 mat 000422 mat 606422 mat 14014422 mat 0.5 - 40422 mat 5.6 46422 mat 15.2 414422 mat 0.5 - 4 0.9 022 mat 5.6 4 6.8 022 mat 15.2 4 11.6 022 mat 121 mat

MCol.bot 00 1.7 - 022 mat 60 4.5 022 mat 140 18.6 022 mat 000 5.5 - 22 mat 606 5.5 - 22 mat 14014 5.5 - 22 mat 0.9 5.5 - 0 5.5 - 22 mat 6.7 5.5 - 6 5.5 - 22 mat 11.7 5.5 - 14 5.5 - 22 mat 0.9 5.5 - 1.7 - 022 mat 6.7 5.5 - 4.5 022 mat 11.7 5.5 - 18.6 022 mat 121 mat

MCol.bot 00 1.7 - 022 mat 60 4.5 022 mat 140 18.6 022 mat 000 5.5 - 22 mat 606 5.5 - 22 mat 14014 5.5 - 22 mat 0.9 5.5 - 0 5.5 - 22 mat 6.7 5.5 - 6 5.5 - 22 mat 11.7 5.5 - 14 5.5 - 22 mat 0.9 5.5 - 1.7 - 022 mat 6.7 5.5 - 4.5 022 mat 11.7 5.5 - 18.6 022 mat 121 mat

Upper column

Bottom column

Upper Vertical lines

Bottom Vertical lines

Far end of upper column.

Far end of bottom column.

Call Program 40: Plot UPPER column moment string values PTS.top nn3 Cords.top MSTR.top Plot_Pts :

Call Program 40: Plot BOTTOM column moment string values PTS.bot nn3 Cords.bot MSTR.bot Plot_Pts :

PTS.top 0.9 0256 black 6.8 0226 black 11.6 0 -68 6 black 35 mat

PTS.bot 1.7 - 0486 black 4.5 0426 black 18.6 0 -128 6 black 35 mat

FDN 1

nn3 1

XY Plot Settings for Column Moment Diagram

CASE

nn3 1

XYPlot.XLimMax 5 el L sum m / 8 + :

Y.Col_Max H.LC H.UC Max m / 1 + : 6.5

XYPlot.XLimMin 5 el 6 - :

XYPlot.YLimMin 5 el Y.Col_Max - :

XYPlot.YLimMax 5 el Y.Col_Max :

FDN.cond TXT Fixed Foundation FDN 1 ≡ Pinned Foundation cases : 11 line :

XYPlot.XTick 5 el 2 :

XYPlot.YTick 5 el 1 :

XYPlot5.XYLabel.XLabel X-Axis (m) setprop 1

FDN.cond Fixed Foundation

XYPlot5.XYLabel.YLabel Height (m) setprop 1

font pName XY.labelFont {pName}.XYLabel.LabelFont font setprop :

Trebuchet MS,7pt XYPlot5 XY.labelFont 1

XYPlot5.XYLabel.LabelFontColor brown setprop 1

MyTitle 1st Floor Col BMD: Case nn3 num2str - FDN.cond concat : 1st Floor Col BMD: Case 1 - Fixed Foundation

XYPlot5.Title.Text MyTitle setprop 1

XYPlot5.Title.TitleFont Trebuchet MS,7pt setprop 1

Case number

nn3 1

FDN 1

Foundation Columns Fixed at Base blue light green 1 3 mat FDN 1 ≡ Foundation Columns Pinned at Base black pink 1 3 mat FDN 0.75 ≡ Wrong Input : Pl check Red pink 1 3 mat cases

Check with plot

MCol.top MCol.bot PTS.top PTS.bot 4 1 sys

Upper Column M.col nn3 1 el kNm 252268 - 31 mat

Bottom Column M.col nn3 2 el kNm 4842128 - 31 mat

0 time t.0 - 0.7 s *

Upper Column M.col 11 el kNm 252268 - 31 mat

Bottom Column M.col 12 el kNm 4842128 - 31 mat

Case 1

Upper Column M.col 21 el kNm 326 - 28 - 31 mat

Bottom Column M.col 22 el kNm 6112 - 52 - 31 mat

M.col kNm 252268 - 31 mat 4842128 - 31 mat 326 - 28 - 31 mat 6112 - 52 - 31 mat 43871 - 31 mat 873135 - 31 mat 32 mat

Case 2

Upper Column M.col 31 el kNm 43871 - 31 mat

Bottom Column M.col 32 el kNm 873135 - 31 mat

Case 3

MCol.top 00 2.3 022 mat 60 4.6 022 mat 100 11.4 022 mat 160 13.7 022 mat 000 3.5 22 mat 606 3.5 22 mat 10010 3.5 22 mat 16016 3.5 22 mat 1.2 - 3.5 0 3.5 22 mat 6.7 3.5 6 3.5 22 mat 9.3 3.5 10 3.5 22 mat 17.2 3.5 16 3.5 22 mat 1.2 - 3.5 2.3 022 mat 6.7 3.5 4.6 022 mat 9.3 3.5 11.4 022 mat 17.2 3.5 13.7 022 mat 161 mat