Double Braces Research Articles

Corrugated Box Compression Strength Enhancement

In this study, 5x5x12 single-wall RSC corrugated boxes were strengthened to increase their compression strength using four different methods; horizontal brace, diagonal brace, L-shape corner post, and triangular corner stiffener. All braces are of 2-inch width. Horizontal Brace : Compression strength increased by 9% when the unsupported box height was reduced from 12 inches to 3 inches. Diagonal Brace : Compression strength increased by 8% and 14% for single and double braces, respectively. L-Shape Corner Post : Compression strength increased by 29% and 38% for exterior and interior posts, respectively. Triangular Corner Stiffener : Compression strength increased by 36% when the stiffener depth increased from 0 inch to 9 inches. The interior corner post method was the most effective and most practical.

Analysis of the natural frequencies of oscillations of a planar truss with an arbitrary number of panels

Introduction. Analytical solutions for problems of structural mechanics are not only an alternative approach to solving problems of strength, reliability and dynamics of structures, but also the possibility for simple performance evaluations and optimization of structures. Frequency analysis of planar trusses, most often used in construction and engineering, is an important part of the study of structures. Objectives - development of a three-parameter induction algorithm for deriving the analytical dependence of the natural oscillation frequencies of the truss on the number of panels. Materials and methods. A flat, statically definable truss with one additional external link and double braces has been considered. The inertia properties of the truss are modeled by point masses located in the nodes of the lower straight truss belt. Each mass is assumed to have only one vertical degree of freedom. The stiffness of all truss rods is assumed to be the same. The task is to obtain analytical dependences of the oscillation frequencies of the proposed truss model on the number of panels. The derivation of the desired formulas is performed by the method of induction in three stages - according to the numbers of rows and columns of the compliance matrix, calculated using the Maxwell - Mohr formula and the number of panels. To find common members of the obtained sequences of coefficients, an apparatus was used to compile and solve the recurrent equations of the Maple computer mathematics system. The task of determining frequencies has been reduced to the eigenvalue problem of a bisymmetric matrix. Results. For the elements of the compliance matrix, general formulas have been found, according to which the frequency equations are compiled and solved. It is shown that in the frequency spectra of trusses with different numbers of panels there is always one common frequency (middle frequency) located in the middle of the spectrum. An expression is found for the maximum value of the average oscillation frequency as a function of the height of the truss. Conclusions. The proposed truss scheme, despite its external static indeterminacy and the lattice, which does not allow for the calculation of forces by such methods as the method of cutting nodes and the cross section method, allows analytical solutions for the natural frequencies of loads in the nodes. The obtained formulas have a rather simple form, and some general properties, such as frequency coincidences for different numbers of panels and the presence of an analytically calculated maximum of the average frequency function of the truss height, make this solution convenient for practical structural evaluations.

Analytical calculation of the deflection of a beam truss with double bracing

A statically determinate planar truss has rectilinear belts and a triangular lattice consisting of double braces. The four links make it seemingly statically indeterminate. The derivation of the formula for the dependence of the deflection on its dimensions and the number of panels is given. Forces in rods are determined in symbolic form by cutting out nodes from the solution of a system of linear equations in the system of computer mathematics Maple. To determine the deflection, the Maxwell - Mohr’s formula is used. Rods (except all rigid support) are assumed to be elastic with the same rigidity. The generalization of individual solutions to an arbitrary number of panels is done by induction. Operators of the Maple system from the calculation data yield linear homogeneous recurrence equations for the coefficients of the desired formula. The solutions of these equations give the general terms of the obtained sequences. Formulas for three types of loads are obtained and compared (the uniform loading of the nodes of the lower and upper belts and the concentrated force in the middle of the span). Curves of the dependence of deflection on the number of panels have weakly expressed minima. The dependencies of the forces in the most compressed and stretched rods on the number of panels are derived. Also given are asymptotic estimates for solutions in accordance with the number of panels in fixed spans of the construction and at a given total load.

Reliability Analysis of Lateral Bracing Forces in Metal-Plated Wood Trusses

AbstractThis paper presents a reliability study of metal-plated (MP) wood truss webs laterally braced by single or double braces, and the results provide a reference for amending relevant prescript...

Lower limit in semiclassical form for the number of bound states in a central potential

We identify a class of potentials for which the semiclassical estimate N (semi) =(1/π)∫ 0 ∞dr −V(r)θ[−V(r)] of the number N of (S-wave) bound states provides a (rigorous) lower limit: N⩾{{ N (semi)}}, where the double braces denote the integer part. Higher partial waves can be included via the standard replacement of the potential V( r) with the effective ℓ-wave potential V ℓ (eff)( r)= V( r)+ℓ(ℓ+1)/ r 2. An analogous upper limit is also provided for a different class of potentials, which is however quite severely restricted.

A class of (ℓ-dependent) potentials with the same number of (ℓ-wave) bound states

We introduce and investigate the class of central potentials V CIC (g 2,μ 2,ℓ,R;r)=− g 2 R 2 r R 4ℓ 1+ 1 2ℓ+1 r R 2ℓ+1 2−1+μ 2 −2, which possess, in the context of nonrelativistic quantum mechanics, a number of ℓ-wave bound states given by the (ℓ-independent!) formula N ℓ (CIC) (g 2,μ 2)= 1 π g 2+μ 2−1 μ 2−1 −1 arctan μ 2−1 . Here g and μ are two arbitrary real parameters, ℓ is the angular momentum quantum number, and the double braces denote of course the integer part. An extension of this class features potentials that possess the same number of ℓ-wave bound states and behave as a/r 2 both at the origin ( r→0 +) and at infinity ( r→∞), where a is an additional free parameter.