Moment Equilibrium Conditions Research Articles

Forces associated with pneumatic power screwdriver operation: statics and dynamics

The statics and dynamics of pneumatic power screwdriver operation were investigated in the context of predicting forces acting against the human operator. A static force model is described in the paper, based on tool geometry, mass, orientation in space, feed force, torque build up, and stall torque. Three common power hand tool shapes are considered, including pistol grip, right angle, and in-line. The static model estimates handle force needed to support a power nutrunner when it acts against the tightened fastener with a constant torque. A system of equations for static force and moment equilibrium conditions are established, and the resultant handle force (resolved in orthogonal directions) is calculated in matrix form. A dynamic model is formulated to describe pneumatic motor torque build-up characteristics dependent on threaded fastener joint hardness. Six pneumatic tools were tested to validate the deterministic model. The average torque prediction error was 6.6% (SD = 5.4%) and the average handle force prediction error was 6.7% (SD = 6.4%) for a medium-soft threaded fastener joint. The average torque prediction error was 5.2% (SD = 5.3%) and the average handle force prediction error was 3.6% (SD = 3.2%) for a hard threaded fastener joint. Use of these equations for estimating handle forces based on passive mechanical elements representing the human operator is also described. These models together should be useful for considering tool handle force in the selection and design of power screwdrivers, particularly for minimizing handle forces in the prevention of injuries and work related musculoskeletal disorders.

Computation of Bearing Capacity Factor Nγ-Prandtl's Mechanism

ABSTRACT In this paper, an analysis based on Prandtl's failure mechanism is proposed for the evaluation of bearing capacity factor, Nγ, using the limit equilibrium approach, coupled with Kotter's equation. Except for shape of the failure surface, no other assumptions are needed in the analysis. A methodology based on Kotter's equation and force equilibrium conditions is developed to identify the correct location of pole of the log spiral and hence the unique failure surface. Using moment equilibrium condition, the point of application of passive thrust is determined. The proposed Nγ values are compared with other available theoretical predictions and experimental results. They show a good agreement with some existing theoretical results and also show a better agreement with available experimental results. The analysis shows that pole of the log spiral lies at the footing edge for general shear failure conditions and the point of application of the passive thrust is strongly influenced by angle of soil internal friction.

20S 作用力測定用ゴルフクラブの開発

No one can know how golf players exert forces and moments on the grip handle from the swing motion. Because the club is manipulated by double hands during swing, the upper limbs and the club make a closed multiple-segment loop. In this paper, an instrumented club equipped with strain gauges was proposed to reduce the difficulties of the closed loop problem. The strain sensors provided information about forces or moments, such as 1) torsional moment acting on the grip axis between hands, 2) bending moments at each sensor position, and 3) tensile and compressive axial forces. Unique solution of forces and moments exerted by hands was achieved through force and moment equilibrium conditions using the information. Four varsity golf players volunteered to participate in this study as subjects. They performed tee shots, and they hit the ball as strong as they could. From the results obtained by this study, the both hands acted couple force for angular acceleration of the club, and the top side hands of some subjects acted force which is making acceleration of the club.

Seismic Passive/Active Thrust on Retaining Wall-Point of Application.

ABSTRACT An analysis of seismic passive/active thrust on a retaining wall is proposed, in which Kotter’s equation is used to obtain the distribution of soil reaction on the failure plane. The geometrical conditions in the analysis are similar to those of Mononobe-Okabe’s analysis. The distinguishing feature of the proposed analysis lies in its ability to compute the point of application of the passive/active thrust, for which moment equilibrium condition is effectively utilized. The point of application of the passive/active thrust depends upon a combination of several parameters such as angles of wall friction, soil internal friction, backfill slope, wall back and seismic coefficients of vertical and horizontal acceleration. The computed values of point of passive and active pressure coefficients compare closely with available results and the point of application of the active thrust also compares closely with available experimental results.

A new procedure for computing the factor of safety using the Morgenstern-Price method

By employing the same assumption regarding interslice forces as that used in the Morgenstern-Price method, two concise recurrence relations between interslice forces and interslice moments are derived which satisfy both force and moment equilibrium conditions. The Newton-Raphson method is used for determining the factor of safety and the associated scaling parameter of the interslice force function. Algebraic derivatives required in the solution process are evolved in a recursive manner which can be easily implemented in a computer program. The choices of initial values of safety factor and scaling parameter are suggested. The procedure proposed in this paper proves to be efficient and solutions converge rapidly.Key words: slope, stability, factor of safety, limit equilibrium method.

A new procedure for computing the factor of safety using the Morgenstern-Price method

By employing the same assumption regarding interslice forces as that used in the Morgenstern-Price method, two concise recurrence relations between interslice forces and interslice moments are derived which satisfy both force and moment equilibrium conditions. The Newton-Raphson method is used for determining the factor of safety and the associated scaling parameter of the interslice force function. Algebraic derivatives required in the solution process are evolved in a recursive manner which can be easily implemented in a computer program. The choices of initial values of safety factor and scaling parameter are suggested. The procedure proposed in this paper proves to be efficient and solutions converge rapidly.Key words: slope, stability, factor of safety, limit equilibrium method.

Determination of passive earth pressure coefficients by the method of triangular slices

A new procedure is proposed for determination of passive earth pressure coefficients using triangular slices within the framework of the limit equilibrium method. The potential sliding mass is subdivided into a series of triangular slices, rather than vertical slices as usual, with inclinations of the slice bases to be determined. The forces between two adjacent slices (interslice forces) are expressed in terms of interslice force coefficients, and recursive equations for solving interslice coefficients are derived. By using the principle of optimality, the critical inclinations of slice bases, minimum interslice force coefficients, and passive earth pressure coefficients are determined. A form of function for describing the distribution of interslice force inclination (interslice force function) is suggested and the scaling parameter contained in the function is determined by satisfying the moment equilibrium condition for the final sliding mass. Comparisons are made with other accepted methods and tables for passive earth pressure coefficients are presented for practical use.Key words: passive earth pressure coefficient, retaining walls, limit equilibrium method, the principle of optimality.

Identification of optimal strategies for increasing whole arm strength using Karush–Kuhn–Tucker multipliers

Objective. The purpose of this study was to develop a computer model for identifying muscles critical to improving functional upper extremity strength. Design. A three-dimensional biomechanical model of the upper extremity was developed, and the predictions were compared to maximal arm strength data collected from healthy volunteers. Background. Although several optimization-based mathematical models of the shoulder have been developed, none have utilized the mathematical properties of the Karush–Kuhn–Tucker multipliers to efficiently estimate the effect of strengthening individual muscles on functional strength of the whole arm. Methods. A static three-dimensional biomechanical model of the glenohumeral, radio-humeral, ulno-humeral and wrist joints was developed for predicting maximal hand exertion forces. The model was formulated as a linear program. Constraints consisted of moment equilibrium conditions and limits on maximum and minimum allowable muscle forces. Predicted arm strengths were compared to maximal pull strength measurements made on 10 subjects (5 male; 5 female). The task involved pulling toward the mid-sagittal plane of the body with the arm flexed 45 degrees. The Karush–Kuhn–Tucker variables associated with the maximal limits on muscle force were computed to estimate the effect of altering the strength of individual muscles on functional arm strength. Results. Maximum pull strengths were predicted well by the model. Karush–Kuhn–Tucker values ranged from 0 (for muscles not at their upper force limits) to 0.11 for the flexor carpi radialis and pectoralis major muscles. Karush–Kuhn–Tucker multipliers were found to be insensitive to the assumed specific tension of muscle. Conclusions. Upper extremity strength can be predicted from musculoskeletal geometry and physiology using linear programming. Relevance Karush–Kuhn–Tucker multipliers associated with the muscle force upper limits give insight into the effect of strengthening individual muscles on whole arm exertion strength. Such an analysis may provide insight into the development of optimal rehabilitation protocols.

Limit Equilibrium Slope Stability Analysis Considering Progressive Failure

This paper proposes a slope stability analysis method considering progressive failure based on the limit equilibrium principle. The softening of soil is taken into account and the slip surface of arbitary shape is adopted.Formulation of the ploblem is carried out by using the slice method, and the analysis satisfies both force and moment equilibrium conditions. The basic idea of the proposed method is to define a local factor of safety at the base of each slice. Thus, the number of unknowns increases, and the ploblem becomes more highly undeterminate than those in the conventional slice methods. In order to render the ploblem determi-nate, two simplifying assumptions about the interslice forces and the line of thrust are simultaniously made which are separatly used in the Morgenstern-Price method and the Janbu method. An overall factor of safety is introduced to evaluate the whole stability of a slope. Finally, the results of an example problem show that the proposed analysis method can reasonably represent the actual behavior of the progressive failure of cl Slopes.

Generalized Limit Equilibrium Method and Its Relation to Slip Line Method

It has been shown after mathematical and mechanical investigation that Limit Equilibrium Method (LEM) can be considered as a method to obtain the necessary condition of Slip Line Method (SLM), and that the solution can be obtained under the condition that Fs = 1 and ∂ Fs/∂θ = 0, where Fs is the safety factor and θ is the inclination of the plane on which the safety factor is defined. Next, the generalized LEM (GLEM) is proposed, dealing with the following points: (1) Triangular or quadrangular blocks can be treated; (2) Safety factors are defined also on interblock planes; and (3) All types of plastic problems, slope stability, bearing capacity, and earth pressure are identically formulated. Two situations regarding treatment of the moment equilibrium condition are discussed. GLEM is applied to well-known problems. The results agree well with those obtained by theoretical methods. GLEM can be used to obtain the distribution of earth pressure or bearing capacity. GLEM, like ordinary LEM, is very effective for the practical problems, but GLEM is more theoretical and it can result in more accurate solutions.

Macro-element analysis of skewed and triangular orthotropic thin plates with beam boundaries

A generalized macro-flexibility analysis of stiffened orthotropic skewed and triangular thin plates with beam stiffened boundaries subjected to bending and stretching is presented. The proposed method accounts for minimized number of elements in a domain, i.e. the element size is independent of the final results. This is accomplished by satisfying the equilibrium and compatibility conditions along the nodal lines interconnecting contiguous elements. The solution form and shape functions of element shapes are a combination of Fourier series and polynomials with undetermined coefficients. To obtain a solution of a general domain, the orthotropic triangular and parallelogram macro-plate elements with edge beams, satisfying moment and shear equilibrium conditions along nodal lines, were assembled and analyzed by utilizing compatibility of deflection and slope. The results from the proposed methodology were compared to the ones from the finite element method. Also, the convergence was checked by increasing the number of harmonics. The study indicates that good convergence is observed within the first four harmonics.

A note on the stability analysis of earth dams

All methods of stability analysis of earth dams presently available for design are based on the principle of limiting equilibrium. According to this principle, the available shear strength along a potential sliding surface is reduced by a factor of safety so that the mass contained within the sliding surface and the free surface is in a state of limiting equilibrium. It is well known that the solution to the problem of determining the available shear strength is statically indeterminate. However, an acceptable solution is one that would describe the state of stress along the surface with reasonable assumptions. For the static analysis of dams, where only the value of the factor of safety is needed, any of the existing methods may be used (Bishop, 1952). But when designing for earthquake conditions by the displacement methods, both the factor of safety as well as the resultant shear force vector are needed. At present there are methods which give both of these (Bishop, 1952; Morgenstern and Price, 1965), but these methods need a high speed computer. A graphical method of circular arc analysis which finds both the factor of safety and the resultant shear force vector with surprisingly good agreement with computer results is presented in this Note. As mentioned earlier, the stability analysis is based on limiting equilibrium. Under the circumstances, when the force vectors representing the external forces, the total shearing resistance along the base of the entire sliding surface and the total normal force are drawn, a closed polygon should be produced. At the same time the forces should satisfy the moment equilibrium condition.