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.