f35a0b71-1bbe-41ad-9bd8-17c4189cc13d 688 NDTM Amarasekera 4 5 false false 0 0 decimal

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

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 :

4 - appVersion 1.0.8348.30405 ≡

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 :

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 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 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 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 :

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

Ex 3.3 - Page 44 : Reinforced concrete design to Eurocode 2 : Mosely, Bungey & Hulse - 7th Ed - pal grave macmillan

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

4 upper columns, 4 lower columns and 3 beams

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

Column b.UC 30030030030041 mat mm * : h.UC 35035035035041 mat mm * : b.LC 30030030030041 mat mm * : h.LC 35035035035041 mat mm * : H.UC 3.5 3.5 3.5 3.5 41 mat m * : H.LC 444441 mat m * : 61 line

Beam b.beam 30030030031 mat mm * : h.beam 60060060031 mat mm * : L 64631 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 : 00031 mat

Moment of Inertia

Upper Columna I.UC 112 / b.UC * h.UC (3^* vectorize : mm 4^1.0719 109^* 1.0719 109^* 1.0719 109^* 1.0719 109^* 41 mat

Lower Columna I.LC 112 / b.LC * h.LC (3^* vectorize : mm 4^1.0719 109^* 1.0719 109^* 1.0719 109^* 1.0719 109^* 41 mat

Beams I.beam 112 / b.beam * h.beam (3^* vectorize : mm 4^5.4 109^* 5.4 109^* 5.4 109^* 31 mat

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 5.8969 1.8 00 1.8 11.2969 2.7 00 2.7 11.2969 1.8 00 1.8 5.8969 44 mat

Gk = 25 kN/m, and variable action, Qk = 10 kN/m, uniformly distributed along the beam.

G.k 25 kN m / * :

Q.k 10 kN m / * :

W.max 1.35 G.k * 1.5 Q.k * + (: kN m / 48.75

W.min 1.35 G.k * (: kN m / 33.75

Define Load Patterns for All 4 Cases

Case I

Case II

Case III

Case IV

FF W.max W.min W.max 31 mat W.min W.max W.min 31 mat W.max W.max W.min 31 mat W.min W.max W.max 31 mat 14 mat : kN m / 48.75 33.75 48.75 31 mat 33.75 48.75 33.75 31 mat 48.75 48.75 33.75 31 mat 33.75 48.75 48.75 31 mat 14 mat

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 69.7 - 135.6 12 mat 93.9 - 93.9 12 mat 135.6 - 69.7 12 mat 37.2 22.2 - 22.2 37.2 - 41 mat 32.5 19.4 - 19.4 32.5 - 41 mat 45.3 - 106.7 12 mat 87.5 - 87.5 12 mat 106.7 - 45.3 12 mat 24.2 10.2 - 10.2 24.2 - 41 mat 21.1 8.9 - 8.9 21.1 - 41 mat 66.9 - 147.6 12 mat 115.1 - 79.7 12 mat 102.2 - 46.3 12 mat 35.7 17.4 - 12 24.7 - 41 mat 31.2 15.2 - 10.5 21.6 - 41 mat 46.3 - 102.2 12 mat 79.7 - 115.1 12 mat 147.6 - 66.9 12 mat 24.7 12 - 17.4 35.7 - 41 mat 21.6 10.5 - 15.2 31.2 - 41 mat 45 mat

Case I

Case II

Case III

Case IV

Beam1

Beam 2

Beam 3

Get Support Moments

M.sup M.all 1 M.all rows range 1 L rows range el : kNm 69.7 - 135.6 12 mat 93.9 - 93.9 12 mat 135.6 - 69.7 12 mat 45.3 - 106.7 12 mat 87.5 - 87.5 12 mat 106.7 - 45.3 12 mat 66.9 - 147.6 12 mat 115.1 - 79.7 12 mat 102.2 - 46.3 12 mat 46.3 - 102.2 12 mat 79.7 - 115.1 12 mat 147.6 - 66.9 12 mat 43 mat

Case I Case II Case III
Case IV

Get Column Moments

M.col M.all 1 M.all rows range M.all cols 1 - (M.all cols range el : kNm 37.2 22.2 - 22.2 37.2 - 41 mat 32.5 19.4 - 19.4 32.5 - 41 mat 24.2 10.2 - 10.2 24.2 - 41 mat 21.1 8.9 - 8.9 21.1 - 41 mat 35.7 17.4 - 12 24.7 - 41 mat 31.2 15.2 - 10.5 21.6 - 41 mat 24.7 12 - 17.4 35.7 - 41 mat 21.6 10.5 - 15.2 31.2 - 41 mat 42 mat

Case I

Case II

Case III

Case IV

Textbook Moment Distribution - 4 Iterations

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