Gabled Frames Research Articles

Optimum weight analysis of steel frames with semirigid connections

A fact that should be initially emphasized is that this research work does not mainly aim at development of optimization techniques which have already been well established for some time ago. Our aim here is only to make use of these techniques for another purpose namely; to obtain the optimum weight solution for steel frames using the semirigid connections concept. The purpose of this study was to determine the following: (1) The percent of rigidity of the semirigid connections that would give the optimum steel weight for the common types of steel frame structures. (2) The exact percent of steel saving when using the semirigid connections concept, compared to the classical approach. (3) Which is cheaper, the gable or the portal frame, considering the same condition of loading and geometrical configuration. Also the relative cheapness of the double bay or triple-bay multistory frames having the same number of storys and also same conditions of loading and height of columns and total span. (4) Whether the deflection is a governing parameter which might hinder the benefits of the use of semirigid connections. The problem here is to find the optimum weight of plane semirigid connected steel frames. The objective function is given by the weight of structure in terms of the geometrical properties of the elements and the density of steel. The design variables are the breadth of flange and the height of web for each element. For the portal, the gable, the triple bay three story, and the double bay three story frames the number of design variables are four, four, ten, and ten respectively. The design constraints represent strength and stiffness design code requirements. Side constraints are respected to assure nonviolating of the practical available dimensions. The model is solved using the nonlinear programming techniques. The unconstrained formulation using the interior penalty function technique is selected. Powell's algorithm is chosen for the generation of the search vector, and the quadratic interpolation technique is chosen for the determination of the step size. The conclusions are as follows: (1) The use of semirigid connections will provide a saving in weight equal to 28% in the portal frame for corresponding rigidity ratio (R.R.) of 0.9, and a saving of 19% in the gable frame for a corresponding R.R. of 0.733. (2) The use of semirigid connections will provide a saving in weight of 10.75% in the double bay three story frame for a corresponding R.R = 0.733, and 23% for the triple bay three story frame with a corresponding R.R = 0.75. (3) The variation in the percent of the rigidity of the column to girder connection will not cause a corresponding change in the amount of steel allocated to columns and girders. (4) The saving in weight will occur mainly due to girders rather than columns. (5) The vertical deflections were not regarded as a dominating factor as its value did not exceed the allowable limits.

Gable Frame Design Considerations

A gable frame design is reviewed with regard to the modeling, load specification, and strength evaluation. It is found that the approximation used for the boundary conditions at the column bases should adequately account for the behavior of the foundation and more than one approximation may be necessary. Uneven loading is shown to very significant, and it is recommended that gable frames always be designed for some uneven distribution of load. The question of the correct effective length for the rafter is examined, and a nonlinear analysis or an approximate, but conservative, approach is suggested for gables with significant axial load in the rafter. One method of utilizing a frame buckling analysis in a conventional AISC evaluation is presented. It is suggested that if there is significant axial stress in the rafter, caution should be exercised in the use of specification limitations, which are based on girder behavior where there may have been no axial stress considered in the derivation and testing of the specification limitations.

Static, dynamic and stability analysis of structures composed of tapered beams

A new numerical method is proposed for the static, dynamic and stability analysis of linear elastic plane structures consisting of beams with constant width and variable depth. It is a finite element method based on an exact flexural and axial stiffness matrix and approximate consistent mass and geometric stiffness matrices for a linearly tapered beam element with constant width. Use of this method provides the exact solution of the static problem with just one element per member of a structure with linearly tapered beams and excellent approximate solutions of the dynamic and stability problems with very few elements per member of the structure in a computationally very efficient way. Very detailed comparison studies of the proposed method against a number of other known finite element methods with respect to accuracy and computational efficiency for cantilever tapered beams of rectangular and I cross section clearly favor the proposed method. A continuous beam, a gable frame and a portal frame consisting of tapered members are analyzed by the proposed method as well as by other known methods to illustrate the use of the method to structures composed of tapered beams.

H 形鋼による鉄骨山形ラーメンの弾塑性耐力の研究 : (その 3) 実大ラーメンの鉛直載荷実験による検討

The elasic-plastic behavior of the working stress designed full-scale gable frame against symmetrically vertical load was observed, and was examined using the theories of Part (I) and Part (II) in this study. In this test, the gable frame showed the asymmetrical by swayed elastic-plastic buckling mode before symmetrical failure without showing a local or lateral buckling. This failure load could not be predicted by the theory that we reported in Part (I), for the value of W_<cr>/W_e was below the transition line. This failure mode was, however, well predicted by the theory of Part (II) in which we considered the deteriorated effect of yielding regions, and the critical value of W_<cr>/W_e of this frame was plotted within expanded the transition area in Part (II).

Dynamic Reduction of Structural Models

This paper considers the errors associated with the reduction of the structural static degrees of freedom before performing a dynamic analysis. It is shown that the standard methods of performing the reduction can lead to significant errors especially for the member loads computed in a forced vibration problem. A modified reduction is developed which is shown to significantly reduce the errors. The standard and modified methods are applied to a cantilever beam, a gabled frame, and a piping system.

Automatic design of tapered member gabled frames

A program for calculating member sizes to yield a minimum with grabled frame with tapered members has been developed. The design produced satisfies in all respects the requirements of Appendix D to the 1969 AISC specification which governs the design of tapered members. The frame design is symmetrical about the vertical centerline, although the loading need not by symmetrical. The rafter can have no, one or two changes of taper within its length, at the designer's option. The matrix force method is used to do the analyses necessary in the design process. The problem is solved by finding a design which minimizes frame weight subject to constraints imposed by the design specification,such as maximum stress and maximum width/thickness ratios, to minimum or interior penalty function approach using the variable metric method of Davidon, Fletcher and Powell. A number of example penalty function design are given to show the versatility of the technique, as well as demonstrating the effect parmeters such as purlin spacing, member length, rafter slope and member depth to width ratio have on resulting designs.

Plastic Design Aids for Pinned-Base Gabled Frames

Single-span rigid steel gabled frames are widely used in the construction of structures covering large areas with no obstructions, such as industrial buildings, auditoriums, warehouses, etc. It is the intent of this paper to facilitate the design of such structures by offering charts for the ultimate strength requirements of the frameworks that comprise them. In the case of statically indeterminate structures, such as most rigid frames, the methods of plastic design are more rational procedures than their elastic counterparts and yield lighter, yet perfectly adequate, designs. Furthermore, it is possible to realize additional weight savings by using haunches at the eaves of the frame, which strengthen the structure, and by using different column and rafter sections that result in a more efficient distribution of material. Only pinned-base frames are investigated, since complete end fixity is not only difficult to achieve in practice, but is also expensive. Besides, in the case of a differential settlement, the results are less detrimental to the frame if the bases of the columns are pinned rather than fixed.

Tension-Field Design of Tapered Webs

This paper deals with the formulation of design guides for tapered webs based on post-buckling strength. Following the basic format and approach used in earlier studies and Baslers tension-field model, allowable stress expressions are derived for tapered webs. They are compared with the current AISC Specification. It is shown that for small or even moderately large tapering ratios, the average depth of the tapered segment can be used in the AISC prismatic girder design formula for tapered members. The results of this study can be used in the design of tapered roof girders of the gable frames commonly encountered. Beams and girders having small or moderate tapers comprise over 90% of tapered beams used in practice. The allowable shear stress of such beams may be obtained either by employing the present AISC provision based on tension-field acton, with the average depth replacing the uniform depth, Eq. (1a), or it may be obtained by employing Eq. (17) or(19). The latter expressions will give results that are somewhat more accurate.

Admissible Loads of Gable Frames

The mechanism method and the statical method have been presented in standard texts for plastic analysis and design of gable frames. AISC5 devised charts for both calculating plastic moments and locating plastic hinges of various gable frames subjected to uniform forces with or without wind load. It is understandable that those charts cannot be applied to frames subjected to concentrated loads, simply because the collapse load computed under the concentrated forces is a lower bound on the collapse load of the same structure with equivalent distributed force. Pincus discussed a generalized super-position method in plastic analysis of gable frames for which tedious procedures similar to that of the mechanism method are used to search for cancellation of plastic hinges.In this report, two domains of admissible loads of general gable frames are presented, in which the concentrated forces are independent and the structural dimensions are arbitrary. For given numerical values of structural dimensions and forces of a particular problem, the plastic moment and collapse mode can be simply determined from the appropriate domain; or for the given numerical values of structural dimensions and the magnitude of plastic moment, the possible collapse load of the frame may also be found. It is interesting to note that the condition of a structural collapse may be studied from the relationship of magnitude as well as direction of the independent forces in the domain.

Effective Length of Columns in Gable Frames

Usually, single-story, shed-type buildings utilizing gable frames are braced normal to these frames or otherwise receive lateral support so that sidesway in this direction is inhibited. On the other hand, single story gabled frames are not braced against sidesway parallel to the plane of the frames. In the design of columns, the 1963 AISC Specification requires that an effective length factor larger than unity be used when computing the slenderness ratio in a plane where the frame is not prevented from sidesway.

Analysis of Multi-Span, Gable Frames

Analysis of Multi-Span, Gable Frames

Discussion of “Wang on Multi-Span Gable Frames”

Discussion of “Wang on Multi-Span Gable Frames”

Closure to “Harris on Multi-Span Gable Frames”

Closure to “Harris on Multi-Span Gable Frames”

Preliminary Analysis of Continuous Gable Frames

Charts for the preliminary analysis of continuous gable frames are presented. The study is restricted to two, three, and four equal-span frames of constant cross section subjected to uniformly distributed loads. All relationships are based on the assumption of elastic deformation. Numerical examples are included.

Discussion of “Multiple-Span Gabled Frames”

Discussion of “Multiple-Span Gabled Frames”

Closure to “Multiple-Span Gabled Frames”

Closure to “Multiple-Span Gabled Frames”