Allowable Bending Stress Research Articles

System Factors for Light-Frame Wood Truss Assemblies

Light-frame wood roof assemblies may be stronger than what the current single member design approach suggests because of repetitive member load sharing and partial composite action. These strengthening effects are partially addressed in the National Design Specification for Wood Construction through a repetitive use factor of 1.15, applied to the allowable bending stress for repetitive wood members. This paper examines the effect of load sharing and composite action on wood pitched-roof assemblies through a new analysis model. Individual truss and roof assembly strength distributions were computed using the new model. The results show that slope, span, and other truss characteristics cause significant changes in the system factor for a given roof structure configuration. Computed system factors are presented in terms suitable for working stress and reliability-based design methodologies. Computed working stress design system factors vary from 1.15 to over 1.50 for the roof structures studied, suggesting t...

Editors Note: 1989 AISC Specification (Ninth Edition) Allowable Bending Stress Design Aid (paper by Allen J. Hulshizer)

Editors Note

Performance of Glue-Laminated Preservative-Treated Columns

ABSTRACT SUITABILITY of resin and allowable stress tests were conducted on three composite glulam timber construction posts. The posts, manufactured with Cascophene LT-92 Phenol-Resorcinol resin and No. 2 KD15 southern pine, were fabricated by splicing preservative-treated and untreated glulam sections. The two sections consisted of three or four plies of 50 mm (2 in.) nominal lumber. Suitability of resin was evaluated from the flexural strength of individual laminate finger joints, shear strength of glue lines and delamination of glue lines exposed to cyclic wetting and drying. The resin was found to be suitable for service conditions for post frame construction. Full size specimens of the joint section of three sizes of glulam construction posts were tested in both flexure and compression. The allowable bending stress, allowable compressive stress parallel to the grain, and apparent elastic modulus for the posts with a 150 x 150 mm (6x6 in.) nominal cross-section were 10.83 MPa, 13.17 MPa and 11.47 GPa (1570, 1910 and 1.66 x 10^ psi), respectively. Corresponding values for posts with a 150 x 200 mm (6x8 in.) nominal cross-section were 11.45 MPa, 13.45 MPa and 11.32 GPa (1660, 1950 and 1.64 x 10^ psi), respectively). The apparent elastic modulus and allowable bending stress for posts with 200 x 200 mm (8 x 8 in.) nominal cross-section were 11.73 GPa and 13.86 MPa (1.70 X 10^ and 2010 psi), respectively.

Allowable Bending Stress of Steel Pipes

Allowable Bending Stress of Steel Pipes

COMPARISON OF TWO, GLUE-LAMINATED, CONSTRUCTION POST CONHGURATIONS

ABSTRACT Allowable structural properties were determined for three composite, glue-laminated timber construction posts. The posts consisted of three or four glue-laminated plies of 50 mm (2 in.) nominal No.2 southern pine lumber fabricated by splicing preservative-treated and untreated sections. The splice consisted of lamina end finger joints oriented horizontally (or parallel) with the wide edge of the lamina. Full size specimens through the joint sections of three sizes of posts were tested to determine allowable structural material properties. The allowable bending stress, compressive stress parallel to the grain and apparent elastic modulus determined for the 150x150 mm (6x6 in.) nominal size category were 13.8, 14.8, and 16 900 MPa (2000, 2150, and 2.47x106 psi), respectively. The allowable bending and compressive stress and apparent elastic modulus for the 150x200 mm (6x8 in.) nominal size category were 14.1, 14.8, and 11 400 MPa (2050, 2150, and 1.66x106 psi), respectively. The allowable bending stress and the apparent elastic modulus were 15.5 and 13 900 MPa (2250 and 2.03x106 psi), respectively, for the 200x200 mm (8x8 in.) nominal size category. These results are compared to a product of similar construction. The allowable values determined may not be representative of the entire population of posts using similar materials and resin systems.

Analysis and design of light gage steel roof systems

The lack of a useful and efficient analysis and design method is a hindrance to the widespread acceptance of cold-formed structural steel members as roof purlins in conventionally engineered buildings. This paper outlines a practical method for the analysis and design of roof Z-purlins. The details used in formulation of the design method are described and a practical design example is included. The roofing system is idealized to behave in a manner analogous to a stiffened plate in evaluating the section properties and allowable bending stresses. This idealization is considered appropriate as the roof system is composed of Z-purlins which are supported at intervals by structural framing and has roof decking attached continously to the outer flange. The roof decking is corrugated and serves as diaphragm bracing for the condition of flexural bending of the Z-purlin. The section properties are considered based upon a composite section, the Z-purlin and deck. In evaluating the allowable bending stress, F b, the top flange of the Z-purlin is considered to be fully braced by the roof deck whereas the bottom flange is considered to be unbraced except at supporting frames and interior inflection points.

Allowable Bending Stresses for Overhanging Monorails

In the design of monorails for trolley hoisting devices it is often necessary to extend the monorail out beyond the last available support (as in Fig. 1), so the lifting point is clear of obstructions. Such a monorail supported vertically at two locations can be analyzed as a simple beam with overhang so the maximum bending moment is easily obtained. However, the question of the allowable bending stress immediately presents itself. The intent of this paper is to address the problem and present a simple design solution.

A General Solution for the Governing Bending Equation

The allowable bending stress Fb for most wide-flange sections is governed only by AISC Eq. 1.5-7, and Eq. 1.5-6 never need to be checked for these sections. Those wideflange sections for which Fb is determined by Eq. 1.5-6, and the unbraced lengths for which these forms govern, are easily identified by simultaneous solution of the bending equations for the common roots of length for any given yield stress Fy and bending coefficient Cb. Tables of these sections and a general solution for determining the governing bending equation are presented in this paper. The tables are useful supplements to Stockwells simplification of the bending equations and to Burgett and Tides extension of the use of the beam charts to designs with bending coefficients greater than unity. The tables and their use are presented in the body of this paper; simultaneous solutions of the bending equations for common roots of length are given in the appendix.

Timber Columns in Combined Bending and Tension: Design

A graphical approach is presented for the design of timber columns subjected to combined bending and tension. The proposed set of charts are used to determine the allowable bending stress and stresses in combined bending and axial tension. The method and the equations are based on the National Design Specification for Wood Construction, and Timber Construction Manual. An illustrative example is presented to show the step-by-step design approach.

Nail Laminated Wall Columns from Dimension Lumber

ABSTRACT Twenty nail laminated wall columns were loaded to failure in bending. Each of the three laminae within a column consisted of two nominal 2x6's butted lengthwise, without mechanical fastening between the members. One outside lamina consisted of one 2.44 m (8 ft) and one 1.22 m (4 ft) long piece of lumber; the center lamina consisted of one 1.22 m (4 ft) and one 2.44 m (8 ft) long piece of lumber and the other outer lamina consisted of two 1.83 m (6 ft) pieces. The joints formed between the end butted lumber were thus staggered by 0.61 m (2 ft). All lumber was No. 2 KD Dense Southern Pine. The fasteners used to laterally connect the laminations were twelve penny hot dipped galvanized nails arranged in a staggered pattern. The allowable stress was determined based on an equivalent actual solid-sawn post size; that is 140 mm x 140 mm (5.5 in. x 5.5 in.) for a 6x6 post. An estimated normal duration allowable bending stress of 4.87 MPa (707 psi) was obtained. Comparisons are made to allowable bending stresses obtained for other nail-laminated column designs from recent studies.

Strength of Nail Laminated Columns with Metal Plated Joints

ABSTRACT THE laminated columns tested in this study were manufactured with treated lumber spliced to untreated lumber with 16 gauge splice type truss plates and pneumatically driven nails having the approximate size and diameter of a 12 penny common wire nail. Two configurations and two lumber grades were studied. The lumber grades of the treated as well as untreated lumber were No. 2 KD Southern Pine and No. 2 KD Dense Southern Pine. The post configurations were a 2x4-2x6-2x4 combination intended to replace a solid-sawn 4x6 and a 2x6-2x8-2x6 combination intended to replace a solid-sawn 6x6. The nail laminated columns of this study rated well when compared to the allowable stress of a No.2 SR Southern Pine post which has an allowable bending stress value of 7584 kPa (1100 psi)

Calculating apparent reliability of wood scaffold planks

Current safety requirements of the American National Standards Institute (ANSI A10.8) for wood scaffold planks are rooted in a history of generally good performance. The requirements are prescriptive in nature, making the standard easy to use. However, in its current form the standard prescribes only maximum allowable spans and limits its scope to three plank sizes and three load conditions. It does not specify what constitutes acceptable performance in solid-sawn scaffold planks. Thus, the requirements cannot be applied with uniform reliability to different plank systems. At the request of the ANSI A10.8 Subcommittee, an ad hoc advisory group from the wood industry was formed to address this problem. This paper relates published requirements for wood scaffold planks in codes and standards to the allowable bending stresses published by lumber grading agencies based on a set of assumptions recommended by the ad hoc group. A methodology is proposed, based on requiring equivalent structural reliability, for designing alternative wood-based scaffold planks. It is anticipated that this paper will be useful to producers and users of wood scaffold plank in its illustration of the sensitivity of both performance and reliability estimates to assumed material variability and distribution type. It is hoped that this report will generate discussion, both on the ANSI requirements themselves and on the best methodology to translate those requirements into measures of safety.

Design of Timber Beams: A Graphical Approach

A graphical approach for the design of timber beams is presented. The proposed design charts and the method enable the selection of allowable bending stress that meets the bending, deflection, and shear requirements recommended by the National Forest Products Association. A number of illustrative examples are shown to show the step by step design approach. The method is applicable for both glulam and sawn lumber beams.

Allowable Stress for Bending Members

The allowable bending stress is a very important design parameter. It controls not only the design of beams, but also of columns when subjected to bending in addition to axial load. The following design examples in the AISC Manual show how the allowable bending stress controls the design. This paper presents a table and a formula which would help to find the value of the allowable bending stress, Fb, expeditiously. The table and formula have been derived from AISC equations.

Direct Feasible and Optimal Design of Laterally Unsupported Beams

When a beam is laterally supported throughout its length, the axis of bending is prescribed, and most efficient use of material results if the moment of inertia around that axis is made as large as possible. The only structural restriction is that width-thickness ratios must not become so large as to cause local buckling; of course, architectural and clearance considerations may impose other limitations. Such beams may be rapidly and optimally designed in steel, using either the Section Modulus Tables in the AISC Manual (pgs. 2-7 to 2-20) or the Allowable Uniform Load Tables (pgs. 2-28 to 2- 81). When a beam is laterally unsupported over some of it length further investigation is required, since the beam tends to become unstable and twist or buckle about its weak axis. If the unsupported length is small enough (L less than Lu), design proceeds using the same tables referred to above, although the allowable bending stress may need to be decreased from that allowed for compact sections to 0.60 Fy. Selecting the optimum is still relatively easy.

A Simplified Method for the Flexural Design of Stiffened Hybrid Girders

Hybrid girders are useful when strength is the governing factor in design. Due to the availability of higher strength steels and their structural efficiency, hybrid beams and girders are becoming more and more popular. The behavior of hybrid beams has been under extensive research and reported in various publications. However, there is still very little literature available on the design of hybrid beams. In 1970, Milek presented a comprehensive paper on hybrid girder design according to the 1969 AISC Specification. Recently, Schilling has published a paper which explores the optimal dimensions of both homogeneous and hybrid I-shaped beams due to bending moment only (web slenderness is assumed to be known). The theory and simplified method presented herein consider full unadjusted allowable bending stress in conjunction with reduced web contribution to the section modulus. The Adventage of this exact approach in flexural design of hybrid girders is that the dependency on b (ratio of web area to one flange area) is eliminated. Thus, no guesswork is required and no iterations are performed with respect to b. In other words a direct flexural design is possible by the simplified method. The method can also be applied for the analysis of a hybrid girder when the cross section is given

Simplified Solution to Interaction Equation

According to the requirements of the AISC Specification, there are three equations, Formulas (1.6 1a), (1.6-1b), and (1.6-2), which must be considered in designing a steel column subjected to combined loading. In Formula (1.6-1a), the combined axial and bending stress is limited by stability, while yielding controls the combined stress in Formula (1.6- b). This factor is appropriately known as the amplification factor. The computed bending stress is required to be increased due to the additional bending stress induced by a secondary moment. This moment is caused by the compressive force and the deflection of the column due to moments applied at the ends and/or a transverse loading on the column. The purpose of this paper is to facilitate the calculations required for obtaining the modified bending amplification factor along with the allowable bending stresses of various steels available. It is hoped that with the use of the proposed charts, the time and effort of the designer will be greatly reduced.

Application of AISC Design Provisions for Tapered Members

The use of tapered structural members having tapered depths and/or widths was first proposed by Amirikian for reasons of economy. Typically, tapered members are used in single story structures of one or more bays (Figs. 1a and 1b) and in cantilevered sections of buildings (Fig. 1c). Some low-rise structures also contain tapered members (Fig. 1d). In view of the lack of basic understanding of the behavior of tapered members, as well as design criteria, a joint WRC-CRC subcommittee was established in 1966 to coordinate research studies. In addition, a subcommittee of the MBMA Technical Committee was established in 1973 to facilitate the development of design guides for tapered members. Two previous papers containing design recommendations were a result of the technical guidance of these subcommittees. The major thrust of these papers deal with the formulation of allowable axial stress, allowable bending stress, and combined axial-flexural compression for tapered members. These design recommendations have been incorporated into the AISC Specification as Appendix D. The examples presented here serve to illustrate the use of the design specifications for tapered members as required by AISC Specification Appendix D. There are still several unanswered questions regarding the rational design of tapered member. Three topics of current interest are (1) local buckling limitations, (2) tension flange support requirements,6 and (3) the Cm factor for beam-columns in unbraced frames. The designer must still use experience and sound engineering judgement regarding design procedures not provided by Appendix D of the Specification.

Simplified Approach to AISC Bending Formulas

In Section 1.5.1.4.6a of the AISC Specification1 there are three equations for determining the allowable bending stress in a beam, and the equations to be used depend on the l/rT limits of the beam in question. However, where Cb is greater than one, or for other steel strengths, these equations must be used to determine Fb. In looking at Formulas (1.5-6a) and (1.5-6b) and at their corresponding l/rT limits, it can be noted that all numerical constants are 510 x 103, or multiples thereof. Further, these same expressions contain the variables Fy and Cb, except for Formula (1.5-6b) which is independent of steel strength. Thus, with all of these common terms it would appear that there exists a procedure wherein the mathematics involved could be simplified. To develop that procedure is the intent of this paper.

Bending Behavior of Cylindrical Web Panels

The stress distribution in cylindrical web panels of horizontally curved girders subjected to an applied moment is studied analytically. Both the membrane state of stress in the plane of the web and the web bending stresses resulting from the curvature of the panel are considered. A simplified mathematical model which treats the web as a series of curved strips (arches) is used. Solutions for this model are obtained using the Rayleigh-Ritz method. The influence of curvature on the resulting stresses in curved webs is presented. Recommendations for the allowable bending stresses in curved beams expressed in terms of the web depth-to-thickness ratio as well as limiting web slenderness ratios are established.