DESIGN OF A FOUR STORY STRUCTURAL FRAMEPresented by:
Chathurika Gamage
DESIGN PROBLEM
Utilize moment resistant frame for analysis Four stories Plan dimensions 100ft x 60ft First floor consists of a parking lot, grocery
store and a boutique Three upper floors to be utilized as office
space
*Dimension are in ft
*Dimension are in ft
COLUMNS W610x307
BEAMS W500x300
8 LOAD CASES FOR ANALYSISCASE Number Factors
1 1.4D
2 1.25D+1.5L+0.5S
3 0.9D+1.5L+0.5S
4 1.25D+1.5L+0.4W
5 0.9D+1.5L+0.4W
6 1.25D+1.5S+0.5L
7 0.9D+1.5S+0.5L
8 1.25D+1.5S+0.4W
9 0.9D+1.5S+0.4W
10 1.25D+1.4W+0.5L
11 0.9D+1.4W+0.5L
12 1.25D+1.4W+0.5S
13 0.9D+1.4W+0.5S
14 D+E+0.5L
15 D+E+0.25S
DEAD LOADS
Due to self-weight Super-imposed dead load Loads due to heating/cooling systems Exterior wall loads
EXTERIOR WALL LOADS
Load Type Load (kPa)
Interior finish 0.1
Studs 0.07
Insulation 0.03
Sheathing 0.067
Siding 0.07
Other fixtures 0.03
TOTAL 0.367
ROOF LOADS
Load Type Load (kPa)
Mechanical duct allowance (ceiling) 0.19Insulating Concrete per 10mm 0.06
TOTAL 0.25
FLOOR LOADS
Load Type Load (kPa)
Normal density concrete topping, per 10mm of thickness 0.24
22mm Hardwood flooring, on sleepers, clipped to concrete 0.24
Interior partitions 1Carpets 0.1
Sprinklers 0.03
TOTAL 1.61
LIVE LOAD
First Floor Upper Floors
4.8kPa
2.4kPa
SNOW LOAD
Assumptions:1) 1 in 50 probability of exceedance per
year2) Normal roof with no drift3) Slope of zero
2kPa according to NBCC
SEISMIC LOADS
Assumptions:1) Class C Soil2) Normal importance
0.07kPa according to NBCC
SEISMIC LOADS (CONTINUED…)
SEISMIC LOADS ACTING AT…
SEISMIC LOADS AT 12.2M IN THE Z-DIRECTION
LIMIT STATE DESIGN
Moment Adequacy of Beams and Columns Shear Adequacy of Beams Buckling of Columns
MOMENT ADEQUACY OF BEAMS AND COLUMNS
Beams are supported Columns are unrestrained
…but L<Lu
Since beams and columns were both Class 1 sections
Mr = ¢∙Fy ∙ Zx
Type Mr
Beams 2690kN∙m
Columns 3080kN∙m
SHEAR ADEQUACY OF BEAMS
Vr = 2770kN
BUCKLING OF COLUMNS
kL/r = 19mm
Using the Handbook for Steel Construction:
Cr= 9857kN
ADEQUACY OF MATLAB PROGRAM
SAP Analysis of un-factored dead Load Equilibrium analysis of joints
SAP ANALYSIS
MATLAB RESULTS F1 F2 F3 M1 M2 M3
Nodes KN KN KN KN-m KN-m KN-m
80 -0.308 120.787 -1.058 -1.812 0.000 0.685
76 -0.307 154.586 -0.053 -0.105 0.000 0.683
72 -0.306 154.588 0.054 0.109 0.000 0.680
68 -0.303 120.777 1.060 1.816 0.000 0.673
79 -0.637 211.470 -1.059 -1.815 0.000 1.234
75 -0.637 245.277 -0.054 -0.107 0.000 1.232
71 -0.635 245.286 0.053 0.106 0.000 1.229
67 -0.633 211.540 1.059 1.813 0.000 1.222
78 -0.373 256.989 -1.065 -1.835 0.000 0.788
74 -0.372 290.761 -0.061 -0.131 0.000 0.786
70 -0.371 290.738 0.046 0.084 0.000 0.783
66 -0.365 256.793 1.054 1.795 0.000 0.770
77 1.308 157.921 -1.074 -1.892 0.000 -2.020
73 1.309 191.357 -0.078 -0.199 0.000 -2.022
69 1.311 189.753 0.077 0.098 0.000 -2.026
65 1.319 143.572 1.100 1.836 0.000 -2.042
SAP RESULTS F1 F2 F3 M1 M2 M3
Nodes KN KN KN KN-m KN-m KN-m
80 -0.412 121.471 -1.026 -1.552 0.000 0.912
76 -0.411 156.756 -0.032 -0.066 0.000 0.912
72 -0.411 156.757 0.032 0.061 0.000 0.912
68 -0.411 121.480 1.026 1.546 0.000 0.912
79 -0.901 211.500 -1.024 -1.550 0.000 1.721
75 -0.901 246.782 -0.029 -0.063 0.000 1.721
71 -0.901 246.781 0.035 0.064 0.000 1.721
67 -0.901 211.501 1.028 1.548 0.000 1.722
78 -0.441 255.425 -1.024 -1.546 0.000 0.952
74 -0.441 290.711 -0.030 -0.060 0.000 0.952
70 -0.441 290.710 0.034 0.067 0.000 0.952
66 -0.441 255.434 1.027 1.552 0.000 0.952
77 1.754 158.742 -1.029 -1.536 0.000 -2.691
73 1.754 194.010 -0.037 -0.053 0.000 -2.691
69 1.754 194.012 0.027 0.074 0.000 -2.692
65 1.754 158.718 1.023 1.562 0.000 -2.692
JOINT EQUILIBRIUM
Joints 1, 3 and 11 were analysed…
JOINT 1
Member
F1 (kN)
F2 (kN)
F3(kN)
M1(kNm)
M2 (kNm)
M3 (kNm)
97 4.639 19.191 0.469 0.004 -2.844 13.172
13 0.846 38.838 14.962 -41.335 2.841 0.005
1 -5.485 -58.029 -15.431 41.331 0.003 -13.177
SUM 0 0 0 0 0 0
JOINT 3
Member
F1 (kN)
F2 (kN)
F3(kN)
M1(kNm)
M2 (kNm)
M3 (kNm)
2 -3.245 20.594 -0.067 -0.001 -0.961 -28.912
3 1.136 13.815 -1.245 -0.003 3.946 21.562
19 -0.895 59.904 34.587 -82.835 -2.976 -0.005
99 3.005 -94.313 -33.275 82.839 -0.009 7.355
SUM 0 0 0 0 0 0
JOINT 11
Member
F1 (kN)
F2 (kN)
F3(kN)
M1(kNm)
M2 (kNm)
M3 (kNm)
8 -4.511 20.491 -0.025 0.001 -0.486 -27.120
9 2.001 13.477 -2.027 -0.009 6.196 19.992
20 0.836 40.611 -29.144 21.289 -2.496 0.000
21 -1.136 50.373 14.226 -49.230 -3.208 0.007
107 2.809
-124.95
2 -10.832 27.949 -0.006 7.120
SUM 0 0 0 0 0 0
CONCLUSION AND RECOMMENDATIONS Meets limit state requirements There were many limitations to this project. Limit state
design was done at a very basic level. Since the beams are supported by concrete slabs, other
limit state evaluations such as punching shear adequacy for columns should be considered. Diagonal members were not included for simplicity.
It is recommended that the MATLAB program be modified to handle diagonal members in order to obtain a more structurally adequate system.
Feasibility study should be performed to ensure minimal cost. This would include changing the beam sizes to make sure minimal amount of material is used. Studies such as this can be used for preliminary analysis of the frame system when creating multi story, complex structures.
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