f35a0b71-1bbe-41ad-9bd8-17c4189cc13d 677 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

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

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

Loadind Details

Frames are spaced at 4.5 m

Imposed and Dead loads

Design Loads on Beams

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

q.k_floor 3.0 kN m 2^/ * : g.k_floor 6.2 kN m 2^/ * : 21 line

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

Imposed

Dead

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

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 3 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

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

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

Case I

Case II

Case III

Beam1

Beam 2

Get Support Moments

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

Get Column Moments

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

Case I

Case II

Case III

Compare with results using Moment Distribution Program - With 7 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