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Included Programs for Substitute Frame Analysis by STIFFNESS METHOD

4 appVersion 1.0.8348.30405

4 - appVersion 1.0.8348.30405 ≡

Program 1 : Pairing non-diagonal indices of stiffness matrix B# Pair_STF nr# B# rows 1 - : k 1 nr# (range Z# k el B# k el B# k 1 + el stack : 11 line for Z# 31 line :

Define X.0 00 augment :

Define S.BEAM 422422 mat :

Program 2 : To find the Stiffness Natrix : Calls Program 1fdn#=1 if foundatio column base is FIXED ", fdn#=0.75 if foundation column base is PINNED L# I#.UC I#.LC I#.beam H#.UC H#.LC fdn# Find_K nr L# rows 1 + : j 1 nr (range M# j el 4 E * I#.UC j el H#.UC j el / I#.LC j el fdn# * H#.LC j el / + I#.beam j el L# j el / + j 1 ≡ I#.UC j el H#.UC j el / I#.LC j el fdn# * H#.LC j el / + I#.beam j el L# j 1 - el / + I#.beam j el L# j el / + j 1 nr ltlt I#.UC j el H#.UC j el / I#.LC j el fdn# * H#.LC j el / + I#.beam j 1 - el L# j 1 - el / + cases * : 11 line for STF M# Diag : (Create diagonal matrix ≡ C# 1 nr range : D# C# Pair_STF : (Indices of non-diagonal elements ≡ j Clear j 1 L# rows range M2# j el 2 E * I#.beam j el L# j el / * : (Non-diagonal elements ≡ r j el D# j el 1 el : (Row index of non-diagonal elements ≡ c j el D# j el 2 el : (Column index of non-diagonal elements ≡ STF r j el c j el el M2# j el : (Assign appropriate M2# to STF ≡ STF c j el r j el el M2# j el : (Assign appropriate M2# to STF ≡ 51 line for STF 81 line :

PROGRAM 3 : To find joint moments & ST Z # aa kk Find_ST# j 1 Z rows range : jm j el Z j el aa : st j el kk 1 -^jm j el * - : st 41 line :

For use with Main Program

Program 4 : Any function can be passed to this program Z# # a Arrange j 1 Z# rows range : D j el Z# j el a : 21 line :

Program 5 : Find lower column moments. Valid even if foundation columns have equal or diff heights st d Find_MLC j 1 st rows range a# st j el : A# j el a# d * vectorize : 21 line for A# 21 line :

Program 6 : Calls Program 4 B# Pair nrr B# rows vectorize 1 el 1 - : k 1 nrr (range Z# k el YY k el YY k 1 + el 21 mat : 11 line for YY FF Z# : B# YY FF Arrange 41 line :

Program 7 : Main program to find support moments, upper & lower column moments Calls Programs 3, 4, 5 & 6 ff# K# h#.UC h#.LC I.b I.C I.L fdn# L# NEW_BMM j 1 ff# cols range fem# j el 112 / ff# 1 j el L# 2^* vectorize (* : 11 line for nrr fem# rows vectorize 1 el 1 + : j 1 nrr range M# j el Y j el - j 1 ≡ Y j 1 - el Y j el - j 1 nrr ltlt Y nrr 1 - el cases : 11 line for Y F M# : st fem# Y F K# Find_ST# : stt st Pair : j 1 ff# cols range k 1 L rows range M.sup j k el stt j el k el E * I.b k el * L k el / (transpose S.BEAM * fem# j el k el - fem# j el k el 21 mat transpose + : 11 line for 11 line for Col_bott# I.L h#.LC / vectorize 4 * E * fdn# * : M.LCC st Col_bott# Find_MLC : Col_upp# I.C h#.UC / vectorize 4 * E * : M.UCC st Col_upp# Find_MLC : M.sup M.UCC M.LCC augment 121 line :

Program 9 : Sum of Upper & Lpwer Col Moments M# Sum_Col_M j 1 M# rows range : A# j el M# j 1 el abs M# j 2 el abs + vectorize : 21 line :

Program 8A : MAX ABSOLUTE VALUE : Nested Array of Diff Sizes M# Max_Abs j 1 M# rows (range tmp M# j el : Z# j el tmp abs vectorize Max : 21 line for Z# 21 line :

Program 8B : Min ABSOLUTE VALUE : Nested Array of Diff Sizes M# Min_Abs j 1 M# rows (range tmp M# j el : Z# j el tmp abs vectorize Min : 21 line for Z# 21 line :

Program to find SF, Max Span Moment and Distance to Max Span Moment

PROGRAM 10 : For any Loading Case Find SF, Max Span BM, X_max M# f# L# Param j 1 f# rows range W j el f# j el L# j el * : V1 j el 0.5 W j el * M# j el sum L# j el / (- : V2 j el W j el V1 j el - (- : M.max_span j el V1 j el (2^2 f# j el * / M# j el 1 el + (- : X_max j el V1 j el f# j el / : 51 line for V1 V2 M.max_span X_max 14 mat 21 line :

W f L * ≡

Beam load

V1 W 2 / M.L M.R + (L / - (≡

SF LHS of beam +ve for plot

V2 W V1 - (- ≡

SF RHS of beam -ve for plot

M.max_span V1 2^2 f * / M.L + ≡

Max span moment on beam

X.max V1 f / ≡

Dist to location of Max span moment from LHS of beam support

PROGRAM 11 : Calls PROGRAM 10 : Find SF, Max Span BM & X_max for ALL Loading Cases M# ff L# Find_All j 1 M# rows range M_case j el M# j 1 L# rows range el : B j el M_case j el ff j el L# Param : 21 line for B 21 line :

PROGRAM 12 : Extract All SFF res Calc_SF j 1 res rows range A j el res j el 112 range el : j 1 ≡ B A 1 el : B B A j el stack : if 21 line for B 21 line :

MAX ABSOLUTE VALUE : Nested Array of Diff Sizes M# Abs_Array j 1 M# rows (range tmp M# j el : Z# j el tmp abs vectorize : 21 line for Z# 21 line :

Disabled

Program 13 To round : By Hean Giraud U n Round U trunc U trunc n mod - :

PROGRAM 14 : Extract ALL Max Span BMM res Span_M nc res cols vectorize 1 el : j 1 res rows range A j el res j el 1 nc 1 - (el : 11 line for A 31 line :

PROGRAM 15 : Extract All X-max res X_Max nc res cols vectorize 1 el : j 1 res rows range A j el res j el 1 nc el : 11 line for A 31 line :

Program 16 : Arrange Support moments M# n Arrange_M_Sup1 nc M# rows : j 1 nc range : A1 j el M# n el vectorize transpose j col : 31 line :

Program 17 : BMD for Any Case. Calls Program 16 m#.sup sff L# ff n.case n.b BMD_Any sf1# sff 1 col transpose : m1# m#.sup 1 Arrange_M_Sup1 : j 1 L# rows range x# j el 0 L# j el 0.20 m * range : 11 line for j Clear j 1 x# n.b el rows range A j el m1# n.case el n.b el abs sf1# n.case el n.b el x# n.b el j el * - ff n.case el n.b el x# n.b el j el (2^2 / * + : 11 line for x# n.b el m / A kNm / 12 mat 61 line :

Program 18 : BMD for ALL Case. Calls Program 16 m#.sup sff L# ff BMD_All_Cases n 0 : j 1 ff cols range k 1 L# rows range n n 1 + : A n el m#.sup sff L# ff j k BMD_Any : 21 line for for A transpose 31 line :

Cordinates of Max Span Moment for all Cases - For Plotting

Program 19 : Cordinates of Max Span Moment for all Cases - For Plotting L# Get_L j 1 L# rows range : A# j el 0 j 1 ≡ L# 1 j 1 - (range el (sum cases : 21 line :

Program 20 : Cordinates of Max Span Moments for a single Case x_max# M_span# L# Get_Pts# j 1 x_max# rows range P j el x_max# j el m / L# Get_L m / j el + M_span# j el kNm / 12 mat : 11 line for P 21 line :

Program 21  Calls Program 20 for Cordinates of All cases x_max M_span L# Pts_All_Cases j 1 x_max rows range A j el x_max j el M_span j el L# Get_Pts# : 11 line for A 21 line :

Program 22 : To find dist to each support from LHS L# F n# 0 : j 1 L# rows 1 - (range X j n# + (j n# + 1 + (range el L# 1 j (range el sum : n# n# 1 + : 21 line for X 31 line :

Program 23 : X cordinates to plot xupport moments L1# Sup_Xcord nr L1# rows : k 1 nr range C 0 L1# stack k 1 ≡ 0 L1# F L1# sum stack cases : 11 line for C 31 line :

Program 24 : Get BMD Cases bmd L# ff Find_BMD_Cases nr L# rows : j 1 ff cols range n# j el j nr * nr 1 - (- (: A j el bmd n# j el j nr * (range el transpose eval : 21 line for A 31 line :

Program 25 : Plot BMD for a given CASE n# Plot_BMD j 1 L rows (range A j el BMD transpose n# el j el 1 col L Get_L m / j el + : B j el BMD transpose n# el j el 2 col : C j el A j el B j el augment : D j el C j el 1 col 1 el C j el 2 col 1 el augment : 41 line for D 21 line :

Program 26 : Find absolute values of nested Msup and etc. M# x_cord Find_Abs a# M# abs vectorize vectorize vectorize : b# a# mat2sys sys2mat : x_cord b# augment vectorize 31 line :

Program 27 : Arrange Support Moment values & X cordinates M# x_cord Arrange_M_Sup_All j 1 M# transpose cols range A j el M# transpose j col : B j el A j el x_cord Find_Abs : 21 line for B 21 line :

Program 28 : Labels to plot X# Plot_Labs j 1 X# rows range j 1 ≡ A# j el X# j el 2 el 1 var2str : B# X# j el A# j el 6 red augment eval : 21 line A# j el X# j el 2 el 1 var2str : B# B# X# j el A# j el 6 red augment stack eval : 21 line if for B# 21 line :

Program 29 : Arrange SF values to PLOT x# sf# Arrange_SF sf1 sf# 1 col : sf2 sf# 2 col : sff sf1 sf2 augment vectorize : sff sff mat2sys sys2mat vectorize : j 1 sff rows range : B# j el x# m / sff kN / j el augment : 61 line :

Program 30 :Labels to print SF values on SFD M# Plot_Labs_SF nr M# rows : a# M# 2 col : a# a# 2 round vectorize 1 var2str vectorize : aa# 1 nr range el 6 : bb# 1 nr range el black : M# a# aa# bb# augment 61 line :

Program 31 : Labels to print SF zero x_cordinates on SFD X# Find_Labs_ZeroSF nr X# rows : a# X# m / 2 round vectorize 2 var2str vectorize : b# 1 nr range el 6 : c# 1 nr range el red : d# 1 nr range el 0 : X# L Get_L + m / d# a# b# c# augment 61 line :

Program 32 : Find max value of nested MMsup matrix M# Find_Max_Abs a M# mat2sys sys2mat : a Max vectorize Max 21 line :

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-azis. 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.

Program 33 : X cordinates to plot Column moments L1# Col_X nr L1# rows : k 1 nr 1 + (range C k el 0 k 1 ≡ L1# 1 k 1 - (range el sum cases : 11 line for C 31 line :

Program 34: Plot Column Moments M1# M2# Plot_Col_M j 1 M1# rows range : B j el M1# j row M2# j row stack : 21 line :

Program 35: Stack relevant matrices M# STACK nr M# rows : j 1 nr range j 1 ≡ B M# j el 2 row : B B M# j el 2 row stack : if 11 line for B 31 line :

Program 36: Io plot UPPER Column Moments M# L# n# H# N# SC# Plot_UP_Col_M X.uc_bot N# M# n# el kNm / * SC# L# * m / (sum / L# Col_X m / + (: Y.uc_bot L# rows 1 + 1 matrix : M1.uc_bot L# Col_X m / N# Y.uc_bot * augment : M2.uc_bot X.uc_bot N# Y.uc_bot * augment : M.uc_bot M1.uc_bot M2.uc_bot Plot_Col_M : V1.uc_bot M1.uc_bot : V2.uc_top L# Col_X m / N# H# * m / augment : V.uc_top V1.uc_bot V2.uc_top Plot_Col_M : X.uc_top M# n# el kNm / SC# L# * m / (sum / 0.5 - (* N# * L# Col_X m / + : Y.uc_top H# N# * m / : M1.uc_top X.uc_top Y.uc_top augment : M2.uc_top L# Col_X m / Y.uc_top augment : M.uc_top M1.uc_top M2.uc_top Plot_Col_M : M.uc_connect M1.uc_top M2.uc_bot Plot_Col_M : M.uc_bot V.uc_top M.uc_top M.uc_connect stack 151 line :

Program 37: Io plot LOWER Column Moments M# L# n# H# N# fdn SC# Plot_LOW_Col_M X.uc_bot N# M# n# el kNm / * SC# L# * m / (sum / L# Col_X m / + (: Y.uc_bot L# rows 1 + 1 matrix : M1.uc_bot L# Col_X m / N# Y.uc_bot * augment : M2.uc_bot X.uc_bot N# Y.uc_bot * augment : M.uc_bot M1.uc_bot M2.uc_bot Plot_Col_M : V1.uc_bot M1.uc_bot : V2.uc_top L# Col_X m / N# H# * m / augment : V.uc_top V1.uc_bot V2.uc_top Plot_Col_M : X.uc_top M# n# el kNm / SC# L# * m / (sum / 0.5 - (* N# * L# Col_X m / + fdn 1 ≡ L# Col_X m / cases : Y.uc_top H# N# * m / : M1.uc_top X.uc_top Y.uc_top augment : M2.uc_top L# Col_X m / Y.uc_top augment : M.uc_top M1.uc_top M2.uc_top Plot_Col_M : M.uc_connect M1.uc_top M2.uc_bot Plot_Col_M : M.uc_bot V.uc_top M.uc_top M.uc_connect stack 151 line :

Program 38: Convert Top Col Moments to strings n# M# MStr2.top a# M# 1 col n# el kNm / : b# a# round vectorize var2str vectorize : 21 line :

Program 39: Convert Top Col Moments to strings n# M# MStr2.bot a# M# 2 col n# el kNm / : b# a# round vectorize var2str vectorize : 21 line :

Program 40:To plot labels in column BMD nn3 M1# M2# Plot_Pts A# M1# Plot_Labs_SF : B# A# : C# M2# : j 1 B# rows range B# j 3 el C# j el : 11 line for B# 51 line :

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