Maximum Allowable Stress Research Articles

Fully-Stressed Design for Alternative Loads

The fully-stressed method is used to optimize structures whose members are subjected to bending, such as beams and frames, under the action of alternative load systems. In a fully-stressed design, at every section the section modulus is chosen so that the maximum allowable stress is reached under at least one of the alternative load systems. For statically indeterminate structures, the technique adopted for achieving the design criterion is iterative in nature. The forces and moments in the structure are adjusted to satisfy the conditions of equilibrium between the external and internal forces and at the same time satisfy fully-stressed condition. A mathematical statement of the design problem is presented for the case of a two-span indeterminate beam under alternative load systems. A sample problem illustrates the application of the method to obtain an optimum design of the indeterminate beam. Also, the procedure is outlined for obtaining a fully-stressed design of an indeterminate portal frame.

Temperature and thermal stress distributions in concrete primary shields for nuclear reactors

The distribution of temperature and thermal stresses arising from the absorption of nuclear radiation in thick annular concrete shields is analysed. Design criteria are developed relating maximum allowable incident energy fluxes to maximum allowable compression or tension stresses. A typical result for a 4 1 2 ft thick shield is a maximum allowable indicent energy flux of 85 Btu/hr-ft 2, resulting in a maximum temperature rise of 95°F in a shield cooled by plant container air on both inner and outer surfaces. The results are virtually independent of the nature of the incident radiation whether medium or high energy gammas, or neutrons. Stature, a Fortran digital computer code for the study of thermal stresses arising from the absorption of nuclear radiation in both steel and concrete annuli is described. Use of Stature allows detailed calculation of the temperature and stress distributions in a shield within 12 sec when the computation is performed with the IBM 7090 digital computer.

Temperature and thermal stress distributions in concrete primary shields for nuclear reactors☆

The distribution of temperature and thermal stresses arising from the absorption of nuclear radiation in thick annular concrete shields is analysed. Design criteria are developed relating maximum allowable incident energy fluxes to maximum allowable compression or tension stresses. A typical result for a 4 1 2 ft thick shield is a maximum allowable indicent energy flux of 85 Btu/hr-ft 2 , resulting in a maximum temperature rise of 95°F in a shield cooled by plant container air on both inner and outer surfaces. The results are virtually independent of the nature of the incident radiation whether medium or high energy gammas, or neutrons. Stature, a Fortran digital computer code for the study of thermal stresses arising from the absorption of nuclear radiation in both steel and concrete annuli is described. Use of Stature allows detailed calculation of the temperature and stress distributions in a shield within 12 sec when the computation is performed with the IBM 7090 digital computer.

Minimum weight layouts of elastic, statically determinate, triangulated frames under alternative load systems

The Michell theory for the absolute minimum weight design of triangulated frames under a single load system is extended to allow for alternative load systems. Only minimum-weight statically-determinate frames, designed to maximum allowable stresses, are discussed. Three simple examples are given to illustrate the manner in which the layouts of such frames may be obtained.

Stress and Strain Limits on the Attainable Velocity in Mechanical Vibration

The maximum peak velocity which can be developed at the free end of a slender rod driven at resonance in a normal mode of longitudinal vibration is given by v0 = c0Sxx, where c0 is the Young's-modulus speed of sound (E/ρ)12 and Sxx is the limiting value of extensional strain for the rod material. The ratio of allowable stress to the maximum peak velocity is given by Txx/v0 = ρc0, where the characteristic specific impedance plays in this case the role of a transfer impedance relating the stress at a node to the velocity at an antinode. The same expressions describe, within half an order of magnitude, the relations between the maximum allowable stress or strain and the normal component of velocity at the antinodes of displacement for thin uniform bars or plates and for wedges or cones vibrating in flexure, and for an exponential solid horn vibrating longitudinally. By inductive extension it is argued that within the indicated precision the same velocity-strain ratios prevail in the vibration of any elastic body however excited.

Stress and Strain Limits on the Attainable Velocity in Mechanical Vibration

The maximum peak velocity which can be developed at the free end of a slender rod driven at resonance in a normal mode of longitudinal vibration is given by v0 = c0 Sxx, where c0 is the Young's modulus speed of sound (E/ρ)12 and Sxx is the limiting value of extensional strain for the rod material. In a similar way, the ratio of allowable stress to the maximum peak velocity is given by Txx/v0 = ρc0, where the characteristic specific acoustic impedance plays in this case the role of a transfer impedance relating the stress at a node to the velocity at an antinode. Similar expressions, modified only by numerical factors which range from 12 to 2, describe the relations between the maximum allowable stress or strain and the normal component of velocity at the antinodes of displacement for thin bars or plates vibrating in flexure.

Work Capacities of Energy Storage Systems on Basis of Unit Weight and Unit Volume

Abstract In view of current and anticipated interest in conserving weight and space in engineering applications, a study is made of work-per-unit-weight and work-per-unit-volume moduli for energy storage systems. Gasoline engines, solid propellants, electrochemical cells, flywheels, compressed gases, compressed liquids, and stressed solids are evaluated. General analytical expressions for the work moduli are derived. For each such general expression, significant optimizing parameters are selected and methods of optimizing the moduli are presented. Information is included pertinent to the problem of selection of energy storage systems for specific applications. Comparisons are made of the practical maximum values of weight and volume moduli for the considered systems. Limitations of the systems, including maximum allowable stress, are discussed.

Approximate Solutions for Struts Supported by an Elastic Foundation

THE case of a strut supported by a number of elastic supports is one that frequently occurs, in structural analysis; an obvious example from monocoque fuselages is that of the longeron loaded in compression and supported at intervals by frames which deform elastically under lateral load from the longeron. From a stressing point of view, the criterion for strut strength is not usually the critical buckling load but the load required to give maximum allowable stress under conditions of initial end eccentricity or initial free deflexion of one or more of the supports. In the case of a simple unsupported strut, for instance, it is the application of eccentrically applied end load that provides the strength criterion, and not the critical buckling under axial end load. Although the determination of the critical buckling load is interesting from an analytical point of view, and is also useful as a standard of reference, solutions of the ‘stress’ conditions have more practical significance for the stress engineer.

Analysis of Effect of Wire Curvature on Allowable Stresses in Helical Springs

Abstract The author suggests a method for determining the effect of wire or bar curvature on allowable stresses in helical springs, based on the endurance properties of the material. The method is based on the assumption, in agreement with available fatigue-test data, that stress-concentration effects produced by wire curvature may be neglected in calculating the static component of applied stress; also, it is assumed that the relation between the static- and variable-stress components at failure follows a linear law. On this basis, charts are given for determining maximum allowable stress as a function of spring index, ratio of minimum to maximum stress, and ratio between yield point and endurance limit. The effect of sensitivity of the material to stress concentration is taken into account by introducing a sensitivity-index q. Results calculated by means of the equations given show good agreement with results from tests of springs of different indexes. Some of the limitations of the method are discussed, and suggestions are made for future testing work.

Rational Design of Hoisting Drums

Abstract The main problem of hoisting-drum design resolves itself into two parts: determination of flange shape and thickness, and determination of the thickness of the drum body. Other factors, such as brake, clutch, and bearings, have already been investigated and are therefore not considered in this paper. The correct proportioning of drum flanges is obviously dependent upon the side pressure brought to bear against them, by the coils of rope wound about the drum. In other words, flange thickness is a function of (a) rope tension and (b) depth of winding. Previous theoretical investigations have recognized these factors, but have failed to take account of the friction between adjacent coils of rope, and between rope and drum, which tends to hold the coils in position without the aid of the flanges, and have also disregarded the flattening of the inside coils under pressure from the outer layers. This flattening, which is quite appreciable on account of the soft core of hoisting rope, results in a shortening of the inner coils, thereby relieving them of a part of their tension, and reducing the pressure against the flanges. A theoretical formula is deduced for the total pressure against a drum flange caused by the winding-on of rope to a given depth and under a given initial tension. Two other formulœ are then deduced, which relate this total pressure to the flange thickness and the maximum allowable tensile and shearing stresses in the material. By means of these formulæ a flange of the usual straight-sided or the mushroom type may be designed to withstand safely the pressure of the rope wound upon the drum. The drum body is subjected to combined stresses, since it is under compression from the coils wound upon it, under tension due to the lateral pressure against the flanges, and under combined torsion and bending caused by the load which is to be hoisted. Formulæ are derived which may be used to obtain the correct thickness both at the center of the drum, where the normal stresses are greatest, and at the ends of the drum, where the shearing stresses are most prominent. In order to check the theoretical formula for flange pressure, tests were made with small-size rope wound upon a special drum, which was so arranged that the side thrust against one flange could be directly measured while the rope was being wound on or unwound. These tests show conclusively that formulæ for flange pressure which do not take account of rope friction and flattening give excessively large results.