Simplified analysis and design methods for structural members of sofa frames considering fatigue effects

The design of upholstered sofa frames to meet the General Service Administration (GSA) performance test regimen requires that analytical method and design loads be available. A simplified analysis method using beam models to analyze and calculate bending moments of critical structural members in a three-dimensional sofa frame was explored. The GSA performance test regimen load schedules were applied to the frame, and transferred to individual structural members in terms of stepped cyclic load schedules. Maximum bending moment values of each structural member were calculated with beam models for each load level of stepped cyclic load schedules that the members were subjected to. Maximum moment values can be used for member design such as determination of member sizes and stresses. Stepped cyclic load schedules can be used for fatigue performance evaluation of full-size frame structural members. A procedure for estimating frame member sizes and deriving design loads for these members was explored. Design loads in terms of equivalent static bending moments while considering fatigue effects were derived for critical structural members of the sofa frame model. The rational design of upholstered sofa frames to meet the General Service Administration (GSA) performance test regimen FNAE-80–214 (GSA 1998) requires that analytical methods be available to determine the sizes of their structural members. Typical sofa frame constructions and loads were analyzed and documented by Eckelman (1982). It was summarized that the best estimates of load design values for sofas can be obtained from performance test requirements contained in GSA specifications. Simplified design and analysis methods were developed for seat foundation systems. Methods of analysis and design have not been fully developed for entire sofa frames. This is because the frame itself constitutes a complex three-dimensional structure in which the characteristics and, in particular, the rigidity of the joints are largely unknown (Zhang et al. 2000). Therefore, exact solutions of structural analyses of a sofa frame may not be justifiable. A simplified analysis method is desirable for furniture engineers to perform daily quick design calculations to estimate structural member sizes without the need of assistance from expensive structural simulation software. Strength and durability design of upholstered furniture frames to satisfy furniture performance test standards such as GSA regimen requires information such as design loads. A systematic scientific investigation of the loads that act on a sofa frame has never been undertaken in the past. Therefore, there is a scarcity of pertinent quantitative data. Fortunately, furniture frame performance test standards such as GSA performance test regimen FNAE-80–214 A are available. It is used to evaluate strength and durability performance of a furniture frame construction. Thus, the loads of performance tests could be the best available candidates for determining design loads for furniture frame components. A procedure of deriving design loads for sofa frame members considering fatigue effects, i.e., to meet specified frame performance test requirements, for instance a GSA performance test, was explored in this study. Development of such design loads can allow furniture engineers to carry out initial frame design using simple calculations. The objectives of this study were to: 1) propose a simplified beam analysis method in estimating bending moments of structural members in a sofa frame; 2) derive cyclic stepped load schedules for fatigue The authors are, respectively, Graduate Student and Associate Professor, Forest Products Lab., Mississippi State Univ., Mississippi State, Mississippi ([email protected]; [email protected]). This paper was received for publication in August 2005. Article No. 10104. ✳Forest Products Society Member. ©Forest Products Society 2007. Forest Prod. J. 57(9):35-41. FOREST PRODUCTS JOURNAL VOL. 57, NO. 9 35 performance evaluation of each structural member; 3) determine structural member dimensions to satisfy frame performance testing requirements; and 4) derive design loads for estimating cross sectional dimensions of structural members in a sofa frame. Methods Approach In this study, a three-dimensional sofa frame structural representation consisting of critical members was proposed (Fig. 1). GSA bare frame performance testing regimen was proposed as external loads (Fig. 2) for structural analysis of the frame. The simplified structural analysis method, treating each member in the sofa frame as a beam with simple and fixed end support boundary conditions, was proposed. Then, the formulae of the maximum moment in the members as a function of applied loads were derived. Once the formula for moment calculation was obtained for each structural member, sizes of structural members were estimated based on S-N (applied nominal stress vs. log number of cycles to failure) curves of materials considered for the structure and their GSA stepped cyclic load schedules (Zhang et al. 2005). Finally, equivalent static ultimate moments for each structural member were calculated based on estimated member cross section dimensions by setting the stress value equal to modulus of rupture (MOR) in the stress-moment relation. Sofa frame structural representation A structural representation of a three-seat sofa frame (Fig. 1) consists of three basic structural subsystems, namely, a) seat frame system, b) back frame system, and c) side frame system. The seat frame system includes principal structural members: Front and Back Rails, Front and Back Spring Rails, and Stretchers. The back frame system consists of Back Top Rail, Back Posts, and Back Uprights. The side frame system has principal members of Front Stumps, Top Arm Rails, and Bottom Side Rails. The overall dimensions shown in Figure 1 represent the sizes of the most common three-seat upholstered sofa furniture frames. Frame performance tests Furniture performance tests may be defined as accelerated tests that predict the ability of a piece of furniture to fulfill its intended function. Performance test standards such as the GSA performance test regimen FNAE-80–214 A are based on a stepped cyclic load model (variable amplitude loading). This means that tested frame members and joints are subjected to a cyclic stepped load rather than a static load or a constant amplitude cycling load. Figure 2 illustrates five test configurations for evaluating structural durability of upholstered furniture bare frames. Table 1 gives detailed cyclic load schedules for these five tests. In the case of the Top Rails-Front to Back test, three identical front-to-back loads are applied to the Top Back Rail of a sofa frame. These loads are applied at the center-point of the rail and at points 1/6 the length of the rail from each end. The test begins at a load level of 75 pounds per load cylinder; loads are increased in increments of 25 pounds per cylinder after 25,000 cycles have been completed at each load level. The test continues until the back frame system or side frame suffers disabling damage or until a critical level of performance has been achieved. The light-service acceptance level is 75 pounds (25,000 cycles), the medium-service level is 100 pounds (50,000 cycles), and the heavy-service level is 150 pounds (100,000 cycles). Sofa structural member analysis models Figures 3 to 6 illustrate the beam models proposed to estimate bending moments for structural members in a sofa frame. Table 2 lists the structural members and their corresponding models. The span length, L, between two end supports is 72 inches, equal to the overall length of the sofa frame for the Back Top Rail, Front Rail, Front and Back Spring Rails. The span length, L, between two end supports for the Top Arm Rail beam model is 34 inches, equal to the overall depth of the sofa frame (Fig. 1). The cantilever beam lengths were 18, 26, and 26 inches for Front Stumps, Back Posts, and Uprights, respectively. For the beam model calculating moments in stretchers, the letter h is the depth of the Front Rail. The moment in the Bottom Side Rails is the same as the maximum moment in the Back Post. The method of superposition (Ugural 1991) was applied to solve the statically indeterminate beam problems. The Back Rail was not analyzed in this study in considering bending fatigue effects since it is not subjected to significantly high bending stresses. But, it may need to be analyzed considering back-to-front impact loading. Stepped cyclic load schedules for individual frame members Stepped cyclic load schedules for testing different subsystems of a sofa bare frame (Table 1) were applied to corresponding frame member beam models. Therefore, fatigue life Figure 1. — Simplified three-seat sofa frame structural model. Figure 2. — Structural performance test loads of three-seat bare sofa frames.