- Email: [email protected]
Design program for multi-story structures
Compufcn& Shuctuns. Vol. 1977,pp. 547-551. Pcrgmon Press 1977. Printed in Orcal Britain
DESIGN PROGRAM FOR MULTI-STORY
STRUCTURES
ROBERTC. KRUEGER,tCONRADP. HEINS, JR.* and DAVIDR. SCHELLING~ Civil EngineeringDepartment,University of Maryland,CollegePark, MD 20742,U.S.A. (Receiued15 July 1976) Abstract-An efficient and short computer program, STFRD, has been developed to facilitate the structural engineer who is involved in multi-story building design. The programconsistsof three basic parts. The first part of the program performs a preliminary analysis of a frame section of a building using approximate methods to determine forces due to the loads. The loads will consist of uniform dead, live and wind loads. The second part of the program utilizes an iterative process, using the allowable stresses given by the AISC building specifications, to determine member sizes. The third part of the program consists of a matrix analysis of the frame section to determine actual forces on the members, due to the loads. This analysis is used in conjunction with the AISC building codes to verify the adequacy of the member sizes chosen. The programalso has a redesign capability whichis used if the preliminary member sizes are not adequate. The entire procedure has been programmed for use on a UNIVAC 1108computer, FORTRAN IV language. The program may be obtained from the author.
UWRODUC’IlON
The computer programs written today for structural steel design of buildings usually consider one particular facet of the overall design process. Some systems consist of short programs which evaluate member reactions utilizing approximate methods and, therefore, ignore stiffness of the columns, together with an iterative application of the AISC building specifications to determine member sizes. The programs may also consist of an efficient two-dimensional matrix analysis which evaluates the actual member reactions with the AISC building specifications being implemented to verify the stress conditions existing in the loaded structure. Some very worthwhile programs have been developed using these ideas to aid the design engineer. However, no program has yet attempted to effectively combine these ideas into a single design program and remain within the bounds of computer capabilities. The predominant thought behind the design program was to develop a short and efficient design program which contains (1) approximate methods[cl, 51, to determine resulting member forces, (2) on iterative application of the AISC building speciiications[l] to determine member sizes and (3) a two-dimensional matrix analysis [2,7] used in conjunction with the AISC codes to verify the selected member sizes. Within the scheme of the program there is a redesign capability, thus permitting a new selection of member sizes if the initial sizes do not satisfy the AISC specifications. The design process is to be initially performed for vertical and then repeated for combined wind and vertical loads, with the allowable stresses increased as specified by the AISC code. A further innovation in the program is the consideration of building depth in the design process. This, therefore permits a more realistic design of the columns. SCOPEOF TFIEPROGRAM Program capabilities. The primary intent of STFRD
is to allow the rapid analysis and design of buildings on small mini-computer systems without sacrificing aptGraduate Research Assistant. SProfessor. DAssistant Professor.
preciable capability. The program can analyze and design one building bent or frame at a time describing either an interior or exterior frame section. This is in keeping with most current design practices and is in lieu of modeling the building as a three-dimensional space frame which would require excessive core storage and processing time. Specific system capabilities with respect to size of building allowed and design features are given in Tables 1 and 2 respectively. A review of Table 1 indicates the number of members and joints which may be handled in one frame; the number of column and girder sizes are arbitrarily set at 58 and 54 respectively and can easily be increased if adequate direct access storage is available. It is felt and verified by the experience of the authors that these limits are adequate to handle the majority of building designs which are encountered in practice. Table 1. Current program dimension limits 1 2 3 4
Number of members Number of joints Number of column selection sizes Number of girder selection sizes
150 200 58 54
A summary of the design features are exhibited in Table 2 along with a comparison with 11 other representations and popular systems. As can be noted, the STFRD system offers considerably more design capability than six of these systems and compares favorably with 5 of the remaining including 2 of the very large systems (STRUDL, and STRUC V). It must be noted here that comparisons are being made between a system STFRD which was created specifically for the design of buildings using the AISC specifications and more general purpose programs. This demonstrates that it is often possible to increase capability and capacity of a computer program by tailoring that software to a specific application. Program assumptions. The choice of which direction to proceed throughout the building with the analysis is selected by the engineer. Initially, the critical frame section of the building should be analyzed. This is assuming the engineer knows the dimensions of the structure and the loads which are applied to the structure.
R. c.
548
KRUEGER
et
a!.
Table 2. Comparisonof various building design systems
SPSfRESSll
AISC OR second pass
STRESS”
NOW?
STBMl, STlW213
AISC
When the critical frame section is selected, a direction for the major axes of the columns must be assumed. There is really no need to consider more than one possible cross sectional major axes direction for the girders because no matter how the bads are applied to the building, bending always occurs about the same local axis in all girders. However, the columns can bend about either of their cross sectional axes. Therefore, it will be assumed that all columns in the section under analysis will be located so that bending occurs about the same axis of each column. Two load configurations are required for the analysis of a frame section having equal bay lengths and a third will be needed for a frame section having unequal bay lengths. The first load configuration is one having all bays fully loaded. This given maximum compression on all columns and the analysis is performed with and without wind loading. The second, and the third, load con@uration is a checkerboard loading system used to obtain the optimum design for the girders. The checkerboard loading system must be performed twice for a frame section of unequal bay Iengths. First, with one half the girders loaded, and then again with the other half loaded. These colorations are also used with and without wind loading. The program assumes a slab-girder system with only uniform vertical loads applied to the slab. A common practice is to assume a triangular distribution. The lines of distribution of load to the girders are imaginary at an angle of 45” to the girders from the joints and intersect a line parallel to the longest bay dimension. If the bay’s length and depth are equal, then these lines all intersect
at the center of the slab. For the exterior shell, a curtain wall system is assumed with each affected girder carrying half the floor height of load above and below. Interior frame sections will, therefore, carrying more slab load while exterior frame sections will carry more exterior shell load. All interior wall or partition loads will be assumed to be included with the dead load of the slab of each bay. Wind loads are inciuded in the analysis of the building in accordance with the ABC budding spec~~a~ons which abow an increase in allowable stresses by one third, when wind load is considered. As a result, some members may require an increase in size. Wind load will be assumed to be uniform and act perpendicular to the building surface. Tbe distribution of wind load from the surface of the building to the members is easily computed since the wind load only affects the columns at the surface of application. Each exterior column takes half of the wind load, per floor of the frame section, applied to the surface on which it is located. Therefore, interior frame sections will have columns carrying twice the wind load of exterior frame sections. Computer Input. Tire input to the program consists of two parts. The first is a list of girder and column selection sizes and their design properties, which may or may not be changed, for each program run. The second part consists of the information required for the problem(s) being run. The input variables for the program are as follows: Part 1 Cards l-54. Cards punched with girder selection sizes
549
Designprogramfor multi-storystructures and their design properties. (FORMAT (A2, A3, F4.0, F5.0/4F6.0)). Cards 55-112. Cards punched with girder selection sizes and their design properties (FORMAT (A2, A3, F4.0, F5.0, llF6.0/7F6.0)). Part I1 Card 1. A card punched with the number of selections being analyzed using FORMAT (110). The following cards are punched for each of the frame sections analyzed in any run of the program. Card 2. A card which serves as a heading and used to distinguish between each frame section analyzed. (FORMAT (BAE)). Card 3. A card containing a list of variables which generally describe the frame section. They are as follows: NM, The number of members; NJ, The number of joints; NRJ, The number of restrained joints; NSF The number of restrained actions, NW, The number of loaded joints; NLM, The number of loaded members; NDEFLS, The number of implied deflections; NC, The number of columns; NF, The number of floors; NB, The number of bays; SH, The story height, if constant; E, The modulus of elasticity; WW, The weight of the exterior shell; N, The yield stress of the steel; BD, The depth of the bays; ST, Frame section type (Interior = 0, Exterior = 1); CX, Major axis direction of the columns (X-x=0,
x-y=l)
Iter-Units (Ft - Kips = 0, In - Lbs = 1) (FORMAT (1015, 3F10.0/2F.O.O,315) Card 4 to (NJ + 3). Cards containing a joint member, J, the X and Y coordinates of the joint, X(J) and Y(J), and the joint type, JJ(J), for each joint. If joint is a support, then it is specified as SPRT for JT(J). (FORMAT (15, 2F.0.0, A6)). Card (NJ + 4) to. Cards containing a member number, MN, the left joint number JTJ(MN), the right joint member, JTK(MN), the member type, MT(MN) and the distance between lateral supports, SL(MN), if the member is a girder. The member types are GIRDER for girders, INTCOL for interior column and EXTOL for exterior column. (FORMAT (315, A6, F9.0)). Card (NJ +4 t NM) to. Cards containing a member number, MN, the type of load on the member, LT(MN) and the load on the member, W(MN). The load type is either a member load, MEMBER, or a wind load, WINDLD. (FORMAT 15, A6, F1O.O)). Card (NJ+4tNMtNLM) to (NJt3tNMt NLM) t NW. Cards containing a restrained joint number, JN, and actions NRST (1X NRST (2) and NRST (3). NRST corresponds to global X, Y and 2 directions and has a value of 0, an unrestrained action or 1, a restrained action. (FORMAT (415)). Card (NJ+4tNMtNLMtNRJ) to (NJ+3tNMt NLM tNRJ+ JW). Cards containing a loaded joint number, JN, and the loads, LDJ(l), LDJ(2) and LDJ(3), corresponding to loads in the X, Y and 2 global directions. (FORMAT (15,3FlO.O)).
Card (NJ+4tNMtNLMtNRJtNLJ) to (NJt3t NMtNLMtNFUtNLJtNDEFLS). Cardscontaining a restrained joint number, JN, the direction of the deflection 1,2 or 3, corresponding to global X, Y and 2 directions and the displacement of the joint XD. (FORMAT (219,FlO.O)). The units are kept constant by the variable ITER and are self explanatory for most of the variables. However, the units for the variables W(MN) are not exactly obvious. The value of the wind or vertical load on a member, W(MN), has the units of weight per square unit of area. This can be either kips ft* or pounds in.2. The same units are also used for the exterior shell weight, WW. These units are used because of the distributions for wind and vertical loads used in the program. The positive direction for forces is determined by the global coordinate axes. If the resultant force due to an applied load is in the direction of either of the coordinate axes, it is considered to be positive. Computer output. The output from the program is self explanatory and consists of all information concerning each frame section analyzed that is inputted to the program and all essential information calculated by the program. The input to the program is outputted so each frame section analyzed can be identified and also enable the user to verify the input. The remainder of the output, information calculated by the program, consists of three parts. The first is the output from the subroutines using approximate methods to analyze the frame section, The second is the output from the subroutines using the AISC building specifications to determine member sizes. The third is the output from the subroutines involved in the matrix analysis of the frame section. All outputted values have units consistent with what is inputted to the program. There are a few points to be noted concerning the output to the matrix analysis subroutines in the program. The equivalent joint loads for the members due to the loads and the actions of the supports are both evaluated and outputted in terms of the global coordinate system. However, the member actions are evaluated and given as output in terms of each member’s local coordinate system. EXAMPLB
PROBLEM
layout of the frame section used as an example problem is shown in Fig. 1 as a fully loaded system. The The
ty
I-
..,
NM.15 NJ-12
Fig. I. Three story, two bay frame section.
550
R. C. KRUEGERet al. *********IsAMpLE
INPUT**********
*********3 STORY,3 BAYS,INTSEC,X-Y********** 12 0 12 0 12 3 3 10.0 4176000. 21 16 4 30. 0 1 0 5184. 0.0 SPRT 1 0.0 0.0 SPRT 2 30.0 0.0 SPRT 3 60.0 0.0 SPRT 4 90.0 10.0 5 0.0 10.0 6 30.0 10.0 I 60.0 10.0 8 90.0 20.0 9 0.0 20.0 10 30.0 20.0 11 60.0 20.0 12 90.0 30.0 13 0.0 30.0 14 30.0 30.0 15 60.0 30.0 16 90.0 1 SEXTCOL 2 61NTCOL 3 71NTCOL 4 8EXTCOL 5 6GIRDER 6 ‘IGIRDER 7 BGIRDER 5 9EXTCOL 6 1OINTCOL 7 1lINTCOL 8 12EXTCOL 9 lOGIRDER 10 1lGIRDER 11 12GIRDER 9 13EXTCOL 10 14INTCOL 11 15INTCOL 12 16EXTCOL 13 14GIRDER 14 15GIRDER 15 16GIRDER 4WINDLD -0.035 SMEMBER -0.175 6MEMBER -0.175 7MEMBER -0.175 1lMEMBER -0.035 12MEMBER -0.175 13MEMBER -0.175 14MEMBER -0.175 18WINDLD -0.035 19MEMBER -0.105 20MEMBER -0.105 ZIMEMBER -0.105 1 1 1 1 2 1 1 1 3 1 1 1 4 1 1 1
-0.045
Fig. 2. Sampleinput data. input for the frame section is given in Fig 2. The frame section consists of a 3-story, 3-bay, interior frame section having loft stories and a 30ft bay depth on both sides. The bay widths are also 30 ft. In the frame section, there are 21 members with 16 connecting joints including 4 supports, or restrained joints, thus 12 restrained actions. The members of the frame section consist of 12 columns and 9 girders, with the columns located so their minor axes coincide with the global X axis. There are no lateral supports existing along the girders or columns. All bays are fully loaded with downward, thus negative uniform live loads of 75 psf. The roof is also loaded with negative uniform live loads of 30 psf. Dead load is as-
sumed to be 100psf for the bay and 75 psf for the roof. Therefore, the total loads for the bays and roof are 157psf and 109psf, respectively. Wind load exists along the right side of the frame and acts in a negative direction. The wind load is 35psf of wall surface and was obtained from the recommended values given in the table of National Building Code Wind (3). Thus, there are 12 loaded members, no loaded joints and no implied deflections of any joints. The exterior shell has an assumed weight of 45psf of wall surface and is inputted as a negative value since it, too, acts downward. The number of elasticity, E, of the shell has a value of 29,000ksi and the yield stress, Fy, of the steel has a
ssi
Design program for multi-story structnres
value of 36 ksi. Since the units used are feet and kips, all values are inputted with these units. The global coordinate system, (xi, K), which locates the joints, has its origin at the bottom left-hand corner of the frame section and proceeds in the positive directions of the axes. The local member coordinate system (JTJ,., JTK,,,.) is designated by going from left to right along each member, This will be in the direction of the global X axis for the girders and the global Y axes for the columns. The global 2 axis is positive out of the paper and is needed for ro~tion desi~ation. The output gives all necessary information as the program proceeds through the analysis and design process. The estimated member sizes for the girders and columns are first evaluated by using the results of only the approximate method analysis for vertical loads together with the AISC building specifications. After the results of the combined wind and vertical loads are evaluated, the columns are redesigned using the increased allowable stress designated by the AISC codes. Each time the columns are redesigned, as well as when they are initially designed, the value of the interaction equation is computed and given with the column sizes, Before proceeding into the matrix analysis of the frame section with the estimated member sizes, the joints and subsequent actions, restrained are given with a “l”, designating a restrained action in either the global X or Y axis directions or about the global 2 axis. The program proceeds through several loops of the matrix analysis, with and without wind load considered in each loop, increasing the aUowable stresses again when wind load is included. During the matrix analysis of the frame section, equivalent joint loads, joint displacements, actions at the supports, member actions and the total compression on each column are calculated and given as output. The first through the matrix analysis loop uses the estimated member sizes found previously and each successive loop uses the member sizes determined by the preceeding matrix analysis. The results of the matrix analysis are used together with the AISC codes to determine or verify member sizes and this iterative
process is repeated until adequate member sizes for the columns and girders are found. The final task of the program is to calculate the total section weight of the frame. The f&l columns sizes and girder sizes, as well as the total section weight for the frame, evaluated by the program are given in Fig. 3. Actually, this is only the final pages of output from the program. The complete output is too long to present and this data is really all that is really required by the engineer.
REFERENCES
1. American Institute of Steel Construction, Manual of Steel Construction, Seventh Edition (1970). 2. F. W. Beanfait, et al., Computer Methods of Structural Analysis. Prentice-Hall, New Jersey (1970). 3. E. H. Gaylord Jr. and C. N. Gaylord, StructuralEngineering ~a~~boo~. McGraw-Hill, New York (1968)(1972). 4. H. I. Laursen, St~ct~ra~ A~atys~~.McGmw-Hi, New York
(1969). 5. C. H. Norris and J. B. Wilbur, Elementary StructuralAnalysis. McGraw-Hill, New York (1972). 6. M. E. Walmer, Manual of StructuralDesign and Engineering Solutions, Prentice-Hall,New Jersey (1968). 7. N. Willems and W. M. Lucas, Jr., Matrix Analysis for ~t~&tu~ ~ngj~eers Prentice-Hall, New Jersey (1968). 8. ICES STRUDL II, Engi~ee~~g User’s gamut. Vol. 1, Frame Analysis. MIT Dept. of Civil Engineering , R68-91 (Nov. 1968). 9. ICES STRIJDL II, Engineering user’s Manual. Vol. 2, Additional Design and Analysis Facilities, 2nd Ed., MIT Dept. of Civil Eneineerine. R70-77 (June 1971). 10. CEPA Lit&y duil E~gi~e~~n~ Program Applj~ation (CEPA). RockviIIe, Marylaud (1975). 11. Systems Professional Users Manual. Control Data Users Manual Publication No. 8406800, CYEERNET (1974). 12. Structural Engineering System Solver (STRESS) for the IBM 1130(1130-K-03X) Version 2, Users Manual. International Business Machines Corporation, H20-0340.2(1%7). 13. Call/370 Program Library Index. Service Bureau Corporation, Form No. ~-231~1~ (15 July, 1973). 14. CYEERNET Data Services Program Library Catalog. Control Data Corporation, Pub. No. DO3003oMx1A (Apr. 1970). 15. Omnidata Program Library. Omnidata, New York (June 1970).
GIRDER SIZES 5 W 30x 116.0 6 w 30X116.0 7 W 33x 118.0 12 W 30x 116.0 13 W 30x 108.0 14 W 30x116.0 19 W 27 x 84.0 20 W27x 84.0 21 W 27x 84.0 COLUMN SIZES 1w 2W 3W 4W 8W 9w 10 w 11 w 15 w 16 W 17 w 18 W
14x 68. 14x127. 14x127. 14x 68. 12x 53. 12x 99. 12x 99. 12x 53. 12x 40. 12x 40. 12x 40. 12x 40.
INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION INACTION ~UATION REACTION EQUATION INTERACTION EOUATION INTERACTION E@JATION INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION
VALUE = 0.47% VALUE = 0.4360 VALUE = 0.4358 VALUE = 0.4667 VALDE = 0.3655
VALUE = 0.3561 VALUE = 0.3531 VALUE = 0.3612 VALUE = 0.1675 VALUE = 0.3813 VALUE = 0.3758 VALUE = 0.1693
TOTAL SECTION WEIGHT Fig. 3. FinaI design output data.
DESIGN PROGRAM FOR MULTI-STORY
STRUCTURES
ROBERTC. KRUEGER,tCONRADP. HEINS, JR.* and DAVIDR. SCHELLING~ Civil EngineeringDepartment,University of Maryland,CollegePark, MD 20742,U.S.A. (Receiued15 July 1976) Abstract-An efficient and short computer program, STFRD, has been developed to facilitate the structural engineer who is involved in multi-story building design. The programconsistsof three basic parts. The first part of the program performs a preliminary analysis of a frame section of a building using approximate methods to determine forces due to the loads. The loads will consist of uniform dead, live and wind loads. The second part of the program utilizes an iterative process, using the allowable stresses given by the AISC building specifications, to determine member sizes. The third part of the program consists of a matrix analysis of the frame section to determine actual forces on the members, due to the loads. This analysis is used in conjunction with the AISC building codes to verify the adequacy of the member sizes chosen. The programalso has a redesign capability whichis used if the preliminary member sizes are not adequate. The entire procedure has been programmed for use on a UNIVAC 1108computer, FORTRAN IV language. The program may be obtained from the author.
UWRODUC’IlON
The computer programs written today for structural steel design of buildings usually consider one particular facet of the overall design process. Some systems consist of short programs which evaluate member reactions utilizing approximate methods and, therefore, ignore stiffness of the columns, together with an iterative application of the AISC building specifications to determine member sizes. The programs may also consist of an efficient two-dimensional matrix analysis which evaluates the actual member reactions with the AISC building specifications being implemented to verify the stress conditions existing in the loaded structure. Some very worthwhile programs have been developed using these ideas to aid the design engineer. However, no program has yet attempted to effectively combine these ideas into a single design program and remain within the bounds of computer capabilities. The predominant thought behind the design program was to develop a short and efficient design program which contains (1) approximate methods[cl, 51, to determine resulting member forces, (2) on iterative application of the AISC building speciiications[l] to determine member sizes and (3) a two-dimensional matrix analysis [2,7] used in conjunction with the AISC codes to verify the selected member sizes. Within the scheme of the program there is a redesign capability, thus permitting a new selection of member sizes if the initial sizes do not satisfy the AISC specifications. The design process is to be initially performed for vertical and then repeated for combined wind and vertical loads, with the allowable stresses increased as specified by the AISC code. A further innovation in the program is the consideration of building depth in the design process. This, therefore permits a more realistic design of the columns. SCOPEOF TFIEPROGRAM Program capabilities. The primary intent of STFRD
is to allow the rapid analysis and design of buildings on small mini-computer systems without sacrificing aptGraduate Research Assistant. SProfessor. DAssistant Professor.
preciable capability. The program can analyze and design one building bent or frame at a time describing either an interior or exterior frame section. This is in keeping with most current design practices and is in lieu of modeling the building as a three-dimensional space frame which would require excessive core storage and processing time. Specific system capabilities with respect to size of building allowed and design features are given in Tables 1 and 2 respectively. A review of Table 1 indicates the number of members and joints which may be handled in one frame; the number of column and girder sizes are arbitrarily set at 58 and 54 respectively and can easily be increased if adequate direct access storage is available. It is felt and verified by the experience of the authors that these limits are adequate to handle the majority of building designs which are encountered in practice. Table 1. Current program dimension limits 1 2 3 4
Number of members Number of joints Number of column selection sizes Number of girder selection sizes
150 200 58 54
A summary of the design features are exhibited in Table 2 along with a comparison with 11 other representations and popular systems. As can be noted, the STFRD system offers considerably more design capability than six of these systems and compares favorably with 5 of the remaining including 2 of the very large systems (STRUDL, and STRUC V). It must be noted here that comparisons are being made between a system STFRD which was created specifically for the design of buildings using the AISC specifications and more general purpose programs. This demonstrates that it is often possible to increase capability and capacity of a computer program by tailoring that software to a specific application. Program assumptions. The choice of which direction to proceed throughout the building with the analysis is selected by the engineer. Initially, the critical frame section of the building should be analyzed. This is assuming the engineer knows the dimensions of the structure and the loads which are applied to the structure.
R. c.
548
KRUEGER
et
a!.
Table 2. Comparisonof various building design systems
SPSfRESSll
AISC OR second pass
STRESS”
NOW?
STBMl, STlW213
AISC
When the critical frame section is selected, a direction for the major axes of the columns must be assumed. There is really no need to consider more than one possible cross sectional major axes direction for the girders because no matter how the bads are applied to the building, bending always occurs about the same local axis in all girders. However, the columns can bend about either of their cross sectional axes. Therefore, it will be assumed that all columns in the section under analysis will be located so that bending occurs about the same axis of each column. Two load configurations are required for the analysis of a frame section having equal bay lengths and a third will be needed for a frame section having unequal bay lengths. The first load configuration is one having all bays fully loaded. This given maximum compression on all columns and the analysis is performed with and without wind loading. The second, and the third, load con@uration is a checkerboard loading system used to obtain the optimum design for the girders. The checkerboard loading system must be performed twice for a frame section of unequal bay Iengths. First, with one half the girders loaded, and then again with the other half loaded. These colorations are also used with and without wind loading. The program assumes a slab-girder system with only uniform vertical loads applied to the slab. A common practice is to assume a triangular distribution. The lines of distribution of load to the girders are imaginary at an angle of 45” to the girders from the joints and intersect a line parallel to the longest bay dimension. If the bay’s length and depth are equal, then these lines all intersect
at the center of the slab. For the exterior shell, a curtain wall system is assumed with each affected girder carrying half the floor height of load above and below. Interior frame sections will, therefore, carrying more slab load while exterior frame sections will carry more exterior shell load. All interior wall or partition loads will be assumed to be included with the dead load of the slab of each bay. Wind loads are inciuded in the analysis of the building in accordance with the ABC budding spec~~a~ons which abow an increase in allowable stresses by one third, when wind load is considered. As a result, some members may require an increase in size. Wind load will be assumed to be uniform and act perpendicular to the building surface. Tbe distribution of wind load from the surface of the building to the members is easily computed since the wind load only affects the columns at the surface of application. Each exterior column takes half of the wind load, per floor of the frame section, applied to the surface on which it is located. Therefore, interior frame sections will have columns carrying twice the wind load of exterior frame sections. Computer Input. Tire input to the program consists of two parts. The first is a list of girder and column selection sizes and their design properties, which may or may not be changed, for each program run. The second part consists of the information required for the problem(s) being run. The input variables for the program are as follows: Part 1 Cards l-54. Cards punched with girder selection sizes
549
Designprogramfor multi-storystructures and their design properties. (FORMAT (A2, A3, F4.0, F5.0/4F6.0)). Cards 55-112. Cards punched with girder selection sizes and their design properties (FORMAT (A2, A3, F4.0, F5.0, llF6.0/7F6.0)). Part I1 Card 1. A card punched with the number of selections being analyzed using FORMAT (110). The following cards are punched for each of the frame sections analyzed in any run of the program. Card 2. A card which serves as a heading and used to distinguish between each frame section analyzed. (FORMAT (BAE)). Card 3. A card containing a list of variables which generally describe the frame section. They are as follows: NM, The number of members; NJ, The number of joints; NRJ, The number of restrained joints; NSF The number of restrained actions, NW, The number of loaded joints; NLM, The number of loaded members; NDEFLS, The number of implied deflections; NC, The number of columns; NF, The number of floors; NB, The number of bays; SH, The story height, if constant; E, The modulus of elasticity; WW, The weight of the exterior shell; N, The yield stress of the steel; BD, The depth of the bays; ST, Frame section type (Interior = 0, Exterior = 1); CX, Major axis direction of the columns (X-x=0,
x-y=l)
Iter-Units (Ft - Kips = 0, In - Lbs = 1) (FORMAT (1015, 3F10.0/2F.O.O,315) Card 4 to (NJ + 3). Cards containing a joint member, J, the X and Y coordinates of the joint, X(J) and Y(J), and the joint type, JJ(J), for each joint. If joint is a support, then it is specified as SPRT for JT(J). (FORMAT (15, 2F.0.0, A6)). Card (NJ + 4) to. Cards containing a member number, MN, the left joint number JTJ(MN), the right joint member, JTK(MN), the member type, MT(MN) and the distance between lateral supports, SL(MN), if the member is a girder. The member types are GIRDER for girders, INTCOL for interior column and EXTOL for exterior column. (FORMAT (315, A6, F9.0)). Card (NJ +4 t NM) to. Cards containing a member number, MN, the type of load on the member, LT(MN) and the load on the member, W(MN). The load type is either a member load, MEMBER, or a wind load, WINDLD. (FORMAT 15, A6, F1O.O)). Card (NJ+4tNMtNLM) to (NJt3tNMt NLM) t NW. Cards containing a restrained joint number, JN, and actions NRST (1X NRST (2) and NRST (3). NRST corresponds to global X, Y and 2 directions and has a value of 0, an unrestrained action or 1, a restrained action. (FORMAT (415)). Card (NJ+4tNMtNLMtNRJ) to (NJ+3tNMt NLM tNRJ+ JW). Cards containing a loaded joint number, JN, and the loads, LDJ(l), LDJ(2) and LDJ(3), corresponding to loads in the X, Y and 2 global directions. (FORMAT (15,3FlO.O)).
Card (NJ+4tNMtNLMtNRJtNLJ) to (NJt3t NMtNLMtNFUtNLJtNDEFLS). Cardscontaining a restrained joint number, JN, the direction of the deflection 1,2 or 3, corresponding to global X, Y and 2 directions and the displacement of the joint XD. (FORMAT (219,FlO.O)). The units are kept constant by the variable ITER and are self explanatory for most of the variables. However, the units for the variables W(MN) are not exactly obvious. The value of the wind or vertical load on a member, W(MN), has the units of weight per square unit of area. This can be either kips ft* or pounds in.2. The same units are also used for the exterior shell weight, WW. These units are used because of the distributions for wind and vertical loads used in the program. The positive direction for forces is determined by the global coordinate axes. If the resultant force due to an applied load is in the direction of either of the coordinate axes, it is considered to be positive. Computer output. The output from the program is self explanatory and consists of all information concerning each frame section analyzed that is inputted to the program and all essential information calculated by the program. The input to the program is outputted so each frame section analyzed can be identified and also enable the user to verify the input. The remainder of the output, information calculated by the program, consists of three parts. The first is the output from the subroutines using approximate methods to analyze the frame section, The second is the output from the subroutines using the AISC building specifications to determine member sizes. The third is the output from the subroutines involved in the matrix analysis of the frame section. All outputted values have units consistent with what is inputted to the program. There are a few points to be noted concerning the output to the matrix analysis subroutines in the program. The equivalent joint loads for the members due to the loads and the actions of the supports are both evaluated and outputted in terms of the global coordinate system. However, the member actions are evaluated and given as output in terms of each member’s local coordinate system. EXAMPLB
PROBLEM
layout of the frame section used as an example problem is shown in Fig. 1 as a fully loaded system. The The
ty
I-
..,
NM.15 NJ-12
Fig. I. Three story, two bay frame section.
550
R. C. KRUEGERet al. *********IsAMpLE
INPUT**********
*********3 STORY,3 BAYS,INTSEC,X-Y********** 12 0 12 0 12 3 3 10.0 4176000. 21 16 4 30. 0 1 0 5184. 0.0 SPRT 1 0.0 0.0 SPRT 2 30.0 0.0 SPRT 3 60.0 0.0 SPRT 4 90.0 10.0 5 0.0 10.0 6 30.0 10.0 I 60.0 10.0 8 90.0 20.0 9 0.0 20.0 10 30.0 20.0 11 60.0 20.0 12 90.0 30.0 13 0.0 30.0 14 30.0 30.0 15 60.0 30.0 16 90.0 1 SEXTCOL 2 61NTCOL 3 71NTCOL 4 8EXTCOL 5 6GIRDER 6 ‘IGIRDER 7 BGIRDER 5 9EXTCOL 6 1OINTCOL 7 1lINTCOL 8 12EXTCOL 9 lOGIRDER 10 1lGIRDER 11 12GIRDER 9 13EXTCOL 10 14INTCOL 11 15INTCOL 12 16EXTCOL 13 14GIRDER 14 15GIRDER 15 16GIRDER 4WINDLD -0.035 SMEMBER -0.175 6MEMBER -0.175 7MEMBER -0.175 1lMEMBER -0.035 12MEMBER -0.175 13MEMBER -0.175 14MEMBER -0.175 18WINDLD -0.035 19MEMBER -0.105 20MEMBER -0.105 ZIMEMBER -0.105 1 1 1 1 2 1 1 1 3 1 1 1 4 1 1 1
-0.045
Fig. 2. Sampleinput data. input for the frame section is given in Fig 2. The frame section consists of a 3-story, 3-bay, interior frame section having loft stories and a 30ft bay depth on both sides. The bay widths are also 30 ft. In the frame section, there are 21 members with 16 connecting joints including 4 supports, or restrained joints, thus 12 restrained actions. The members of the frame section consist of 12 columns and 9 girders, with the columns located so their minor axes coincide with the global X axis. There are no lateral supports existing along the girders or columns. All bays are fully loaded with downward, thus negative uniform live loads of 75 psf. The roof is also loaded with negative uniform live loads of 30 psf. Dead load is as-
sumed to be 100psf for the bay and 75 psf for the roof. Therefore, the total loads for the bays and roof are 157psf and 109psf, respectively. Wind load exists along the right side of the frame and acts in a negative direction. The wind load is 35psf of wall surface and was obtained from the recommended values given in the table of National Building Code Wind (3). Thus, there are 12 loaded members, no loaded joints and no implied deflections of any joints. The exterior shell has an assumed weight of 45psf of wall surface and is inputted as a negative value since it, too, acts downward. The number of elasticity, E, of the shell has a value of 29,000ksi and the yield stress, Fy, of the steel has a
ssi
Design program for multi-story structnres
value of 36 ksi. Since the units used are feet and kips, all values are inputted with these units. The global coordinate system, (xi, K), which locates the joints, has its origin at the bottom left-hand corner of the frame section and proceeds in the positive directions of the axes. The local member coordinate system (JTJ,., JTK,,,.) is designated by going from left to right along each member, This will be in the direction of the global X axis for the girders and the global Y axes for the columns. The global 2 axis is positive out of the paper and is needed for ro~tion desi~ation. The output gives all necessary information as the program proceeds through the analysis and design process. The estimated member sizes for the girders and columns are first evaluated by using the results of only the approximate method analysis for vertical loads together with the AISC building specifications. After the results of the combined wind and vertical loads are evaluated, the columns are redesigned using the increased allowable stress designated by the AISC codes. Each time the columns are redesigned, as well as when they are initially designed, the value of the interaction equation is computed and given with the column sizes, Before proceeding into the matrix analysis of the frame section with the estimated member sizes, the joints and subsequent actions, restrained are given with a “l”, designating a restrained action in either the global X or Y axis directions or about the global 2 axis. The program proceeds through several loops of the matrix analysis, with and without wind load considered in each loop, increasing the aUowable stresses again when wind load is included. During the matrix analysis of the frame section, equivalent joint loads, joint displacements, actions at the supports, member actions and the total compression on each column are calculated and given as output. The first through the matrix analysis loop uses the estimated member sizes found previously and each successive loop uses the member sizes determined by the preceeding matrix analysis. The results of the matrix analysis are used together with the AISC codes to determine or verify member sizes and this iterative
process is repeated until adequate member sizes for the columns and girders are found. The final task of the program is to calculate the total section weight of the frame. The f&l columns sizes and girder sizes, as well as the total section weight for the frame, evaluated by the program are given in Fig. 3. Actually, this is only the final pages of output from the program. The complete output is too long to present and this data is really all that is really required by the engineer.
REFERENCES
1. American Institute of Steel Construction, Manual of Steel Construction, Seventh Edition (1970). 2. F. W. Beanfait, et al., Computer Methods of Structural Analysis. Prentice-Hall, New Jersey (1970). 3. E. H. Gaylord Jr. and C. N. Gaylord, StructuralEngineering ~a~~boo~. McGraw-Hill, New York (1968)(1972). 4. H. I. Laursen, St~ct~ra~ A~atys~~.McGmw-Hi, New York
(1969). 5. C. H. Norris and J. B. Wilbur, Elementary StructuralAnalysis. McGraw-Hill, New York (1972). 6. M. E. Walmer, Manual of StructuralDesign and Engineering Solutions, Prentice-Hall,New Jersey (1968). 7. N. Willems and W. M. Lucas, Jr., Matrix Analysis for ~t~&tu~ ~ngj~eers Prentice-Hall, New Jersey (1968). 8. ICES STRUDL II, Engi~ee~~g User’s gamut. Vol. 1, Frame Analysis. MIT Dept. of Civil Engineering , R68-91 (Nov. 1968). 9. ICES STRIJDL II, Engineering user’s Manual. Vol. 2, Additional Design and Analysis Facilities, 2nd Ed., MIT Dept. of Civil Eneineerine. R70-77 (June 1971). 10. CEPA Lit&y duil E~gi~e~~n~ Program Applj~ation (CEPA). RockviIIe, Marylaud (1975). 11. Systems Professional Users Manual. Control Data Users Manual Publication No. 8406800, CYEERNET (1974). 12. Structural Engineering System Solver (STRESS) for the IBM 1130(1130-K-03X) Version 2, Users Manual. International Business Machines Corporation, H20-0340.2(1%7). 13. Call/370 Program Library Index. Service Bureau Corporation, Form No. ~-231~1~ (15 July, 1973). 14. CYEERNET Data Services Program Library Catalog. Control Data Corporation, Pub. No. DO3003oMx1A (Apr. 1970). 15. Omnidata Program Library. Omnidata, New York (June 1970).
GIRDER SIZES 5 W 30x 116.0 6 w 30X116.0 7 W 33x 118.0 12 W 30x 116.0 13 W 30x 108.0 14 W 30x116.0 19 W 27 x 84.0 20 W27x 84.0 21 W 27x 84.0 COLUMN SIZES 1w 2W 3W 4W 8W 9w 10 w 11 w 15 w 16 W 17 w 18 W
14x 68. 14x127. 14x127. 14x 68. 12x 53. 12x 99. 12x 99. 12x 53. 12x 40. 12x 40. 12x 40. 12x 40.
INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION INACTION ~UATION REACTION EQUATION INTERACTION EOUATION INTERACTION E@JATION INTERACTION EQUATION INTERACTION EQUATION INTERACTION EQUATION
VALUE = 0.47% VALUE = 0.4360 VALUE = 0.4358 VALUE = 0.4667 VALDE = 0.3655
VALUE = 0.3561 VALUE = 0.3531 VALUE = 0.3612 VALUE = 0.1675 VALUE = 0.3813 VALUE = 0.3758 VALUE = 0.1693
TOTAL SECTION WEIGHT Fig. 3. FinaI design output data.