Torsional Distortion Research Articles

Analysis of continuous box girder bridges including the effects of distortion

Torsional warping and distortion of the cross-section are important features of thin-walled beams and must be considered fully in the design of box girder bridges. A method of elastic analysis is developed based on the stiffness approach which includes the effects of warping torsion and distortion in addition to the more familiar actions of bending moment and torsion. The method, which is applicable to straight single cell box girders with at least one axis of symmetry, is demonstrated here in the analysis of three different box girder models for which experimental or analytical results were already available. The method is shown to be easy and economical to use and provides a physical insight into the structural response of thin-walled box girder bridges under general loading conditions.

Thin‐Walled Multicell Box‐Girder Finite Element

A thin‐walled‐box‐girder finite element that can model extension, flexure, torsion, torsional warping, distortion, distortional warping, and shear lag effects was developed using an extended version of Vlasov's thin‐walled beam theory. The element has two end nodes, but it has besides the six nodal degrees of freedom of a conventional beam element, additional degrees of freedom to account for torsional warping, distortion, distortional warping, and shear lag. The governing differential equation pertaining to each action was used to derive the exact shape functions and the stiffness matrix and nodal load vector of the element. An orthogonalization procedure was employed to uncouple the various distortional and shear lag modes. A numerical example was solved that compared the proposed method with the facet‐shell finite element analysis, with good agreement between the two sets of results.

Spectroscopy and structure of quadruply bonded complexes under extreme pressure (Re2X82-, Mo2Cl4(PMe3)4)

Application of pressure (up to 150 kbar, where 1 kbar = 986.9 atm = 0.1 GPa) to solutions of Re{sub 2}X{sub 8}{sup 2{minus}} (X = F, Cl, Br) and Mo{sub 2}Cl{sub 4}(PMe{sub 3}){sub 4} results in smooth, continuous changes in experimental observables related to metal-metal bond length and, for the Re complexes, torsional angle (X-Re-Re-X dihedral angle). Resonance Raman studies show that increasing pressure engenders an increase in the frequency of the metal-metal stretching mode for all of the species studied, and this change is empirically correlated with a decrease in metal-metal bond length. Large red shifts in the energy of the {sup 1}({delta} {yields} {delta}*) transitions with increased pressure for Re{sub 2}Br{sub 8}{sup 2{minus}} and Re{sub 2}Cl{sub 8}{sup 2{minus}}, in contrast to the relative insensitivity of Re{sub 2}F{sub 8}{sup 2{minus}} absorption and Mo{sub 2}Cl{sub 4}(PMe{sub 3}){sub 4} fluorescence transitions, imply a tendency for the former complexes to distort torsionally from an eclipsed configuration toward a staggered configuration due to pressure-induced steric repulsion of the chloride and bromide ligands. Integrated absorption intensities further show that, at higher pressures, even Re{sub 2}F{sub 8}{sup 2{minus}} undergoes some torsional distortion, whereas the steric repulsion of adjacent phosphines located at a 90{degree} dihedral anglemore » on opposite Mo atoms prevents Mo{sub 2}Cl{sub 4}(PMe{sub 3}){sub 4} from distorting along the torsional coordinate. 28 refs., 7 figs., 1 tab.« less

ChemInform Abstract: Determination of the Molecular Structure of Tris(trimethylsilyl)amine in the Gas Phase by Electron Diffraction.

The structure and conformation of tris(trimethylsilyl)amine in the gas phase have been determined by electron diffraction. The three Si–N bonds are coplanar and 175.5(3) pm long (ra). The trimethylsilyl groups are arranged so that the overall symmetry for the heavy atoms is very close to C3h, with twists of just 5.2(24)° reducing the symmetry to C3. The errors in parentheses are each one standard deviation, so this torsional distortion is barely significant. The trimethylsilyl groups had local Cs symmetry, with two NSiC angles of 111.5(7) and one of 112.6(4)°, and two CSiC angles 108.0(8)° and the other one thus 105.0°. Other major parameters are r(Si–C) 187.9(3) pm, r(C–H) 110.6(3) pm, and SiCH 110.1(4)°.

Determination of the molecular structure of tris(trimethylsilyl)amine in the gas phase by electron diffraction

The structure and conformation of tris(trimethylsilyl)amine in the gas phase have been determined by electron diffraction. The three Si–N bonds are coplanar and 175.5(3) pm long (ra). The trimethylsilyl groups are arranged so that the overall symmetry for the heavy atoms is very close to C3h, with twists of just 5.2(24)° reducing the symmetry to C3. The errors in parentheses are each one standard deviation, so this torsional distortion is barely significant. The trimethylsilyl groups had local Cs symmetry, with two NSiC angles of 111.5(7) and one of 112.6(4)°, and two CSiC angles 108.0(8)° and the other one thus 105.0°. Other major parameters are r(Si–C) 187.9(3) pm, r(C–H) 110.6(3) pm, and SiCH 110.1(4)°.

ChemInform Abstract: A Laser Flash Photolysis Study of 2,6‐Dimethyl‐3,5‐diphenyl‐4‐pyrone and Related Chromones. Evidence for Triplet State Structural Relaxation from Quenching Behaviors.

The 308- or 337.1-nm laser excitation of 2,6-dimethyl-3,5-diphenyl-4-pyrone (1), 2-phenylchromone (2), and 2,3-diphenylchromone (3) results in the formation of short-lived triplets (tau/sub 0//sup T/ = 1-5 ..mu..s, lambda/sub max//sup T/ = 330-365 nm) in high yields (0.5-1.0 in benzene). From phosphorescence spectra at 77 K, the spectroscopic triplet energies of these aromatic enones are estimated at 69, 62, and 67 kcal mol/sup -1/, respectively. However, in fluid solutions at room temperature, the triplets are poorly quenched by 1-methylnaphthalene (E/sub T/ = 59.6 kcal mol/sup -1/), dienes (E/sub T/ approx. = 59 kcal mol/sup -1/), and ferrocene (E/sub T/ approx. = 40 kcal mol/sup -1/). In spite of the apparent exothermicity, the energy-transfer processes are inefficient; this suggests geometric distortion in these triplets, very probably in the form of partial twisting about the ene double bonds, causing a lowering of vertical energy (at relaxed geometry) by approx.30 kcal mol/sup -1/. The quenching behavior of the triplet of 2, however, is normal, the rate constants for quenching by the above-mentioned quenchers being in the limit of diffusion control. A major reason for the excited-state torsional distortion in 1 and 3 appears to be the steric interaction between adjacent substituents (phenyl and methyl)more » on the carbon atoms of the ene double bond.« less

Structural Aspects of the Lattice Thermal Expansion of Hexagonal Cordierite

The mechanism of lattice thermal expansion in pure hexagonal cordierite prepared by glass devitrification was investigated by time‐of‐flight neutron powder diffraction at temperatures from 22° to 750°C under vacuum. Full matrix least‐squares refinement of the diffraction spectra was carried out in space group P6/mcc using the Rietveld method. The structural data from the refinements were resolved into components parallel and normal to the c axis. The negative c axis expansion results from two effects: (1) increasing distortion of the T2 tetrahedral (ring tetrahedra) with temperature, primarily due to displacement of the T2 cations toward the c‐axis channels in the structure; (2) decreasing distortion of the T1/M tetrahedra/ octahedra with increasing temperature, due to octahedral I (M‐O1) bond expansion and an associated decrease in torsional distortion of the T1 tetrahedra.

A laser flash photolysis study of 2,6-dimethyl-3,5-diphenyl-4-pyrone and related chromones. Evidence for triplet state structural relaxation from quenching behaviors

The 308- or 337.1-nm laser excitation of 2,6-dimethyl-3,5-diphenyl-4-pyrone (1), 2-phenylchromone (2), and 2,3-diphenylchromone (3) results in the formation of short-lived triplets (tau/sub 0//sup T/ = 1-5 ..mu..s, lambda/sub max//sup T/ = 330-365 nm) in high yields (0.5-1.0 in benzene). From phosphorescence spectra at 77 K, the spectroscopic triplet energies of these aromatic enones are estimated at 69, 62, and 67 kcal mol/sup -1/, respectively. However, in fluid solutions at room temperature, the triplets are poorly quenched by 1-methylnaphthalene (E/sub T/ = 59.6 kcal mol/sup -1/), dienes (E/sub T/ approx. = 59 kcal mol/sup -1/), and ferrocene (E/sub T/ approx. = 40 kcal mol/sup -1/). In spite of the apparent exothermicity, the energy-transfer processes are inefficient; this suggests geometric distortion in these triplets, very probably in the form of partial twisting about the ene double bonds, causing a lowering of vertical energy (at relaxed geometry) by approx.30 kcal mol/sup -1/. The quenching behavior of the triplet of 2, however, is normal, the rate constants for quenching by the above-mentioned quenchers being in the limit of diffusion control. A major reason for the excited-state torsional distortion in 1 and 3 appears to be the steric interaction between adjacent substituents (phenyl and methyl)more » on the carbon atoms of the ene double bond.« less

Bracing for composite box girder bridges

For steel–concrete composite box girder bridges, the steelwork is generally erected first and then the concrete deck cast. During construction the girder may be subjected to a variety of construction loads. If the girder is a flexible open section, and lacks distortional or torsional stiffness, the cross section will deform or twist excessively; such difficulties with box girder construction have been reported. Bracing systems should be installed to increase the torsional and distortional stiffness of the open section during construction. A finite strip analysis of the influence of bracing systems on open section box girders is presented and compared with test results obtained using a one-quarter scale model. With the analysis, the influence of ties, distortional bracing, torsion boxes, and top chord bracing on the behaviour of torsionally open box girders is examined. Simplified design methods are also presented whereby the bracing forces and the stresses arising from the distortion of the section can be computed. Key words: bridges (box girder), bridges (steel), box beams, torsional distortion, bending distortion, bracing, construction safety.

A vibronic analysis of the lower à 1A″←X̃ 1A′ singlet–singlet and ã 3A″←X̃ 1A′ triplet–singlet band systems of thioacrolein (2-propenethial)

The visible spectrum of thioacrolein has been photographed under conditions of long path lengths 98 m and modest dispersion (15 nm cm−1). Two electronic systems have been identified in the spectrum, namely, the ã 3A″←X̃ 1A′ spin forbidden but orbitally allowed n→π* transition and its fully allowed companion transition à 1A″←X̃ 1A′. The vibrational fine structure in both transitions is assigned in terms of a single quantum of ν10(CS), ν11(CC), ν12(CCS), and sequence transitions in ν18 (torsion). The structural changes which accompany the electronic excitation are interpreted in terms of a shortening of the CC bond, a lengthening of the CS bond and a stiffening of the skeleton to torsional distortion. No evidence for cis thioacrolein has been found.

Catalytic conformation of carboxypeptidase A: The structure of a true reaction intermediate stabilized at subzero temperatures

The structure of the mixed anhydride, acyl-enzyme intermediate of the esterolytic reaction of carboxypeptidase A is characterized by application of cryoenzymologic, magnetic resonance, and molecular graphics methods with use of the Co 2+-substituted enzyme and the specific spin-label ester substrate O-3-(2,2,5,5-tetra-methylpyrrolinyl-1-oxyl)-propen-2-oyl- l-β-phenyllactate. A radial separation of 7·7 Å between the active site Co 2+ and the nitroxide group in the low temperature-stabilized acyl-enzyme intermediate is determined on the basis of their spin-spin (dipole-dipole) interactions. Application of molecular graphics techniques shows that the only configuration of the substrate that is sterically accommodated by the active site yields a calculated metal ion-to-nitroxide distance of 7·8 Å. Steric accommodation of the spin-label in the active site requires severe torsional distortion around the aliphatic double bond of the propenoyl side-chain. Examination of the structure of the enzyme: spin-label intermediate reveals that the distortion arises from steric interactions of the pyrrolinyl group with the protein at a position that corresponds to the site occupied by the penultimate amide residue of an oligopeptide substrate from the site of cleavage. Together with kinetic data showing that hydrolysis of the spin-label is governed by rate-limiting deacylation, the results indicate that geometric distortion of substrates by secondary interactions with the enzyme, in general, is an obligatory part of the catalytic action of carboxypeptidase A. When viewed with respect to requirements for stereoelectronic control of bond cleavage in tetrahedral adducts of esters and amides (Deslongchamps, 1975) the results suggest that torsional distortion during catalysis results in rotation around the scissile bond of the substrate, and that this rotation is required to form the mixed anhydride reaction intermediate. These findings further support the interpretation that the hydrolysis of esters and amides catalyzed by carboxypeptidase A proceeds according to similar mechanisms except that formation of the mixed anhydride is rate-determining in peptide hydrolysis while deacylation of the mixed anhydride is rate-limiting in ester hydrolysis. Additionally, in this study application of the extension of the theory of the Solomon-Bloembergen-Morgan equations derived by Lindner (1965) for paramagnetic metal ions with S ≥ 1 demonstrates that the zero-field splitting of the high-spin Co 2+ in the metal-substituted enzyme has no significant influence in determination of the relaxation enhancement of solvent protons by the active site metal ion.

Dislocations in Homoepitaxial Layers on "Dislocation Free" LEC-GaP Substrates

Abstract Dislocation structures in S-and N-doped homoepitaxial layers on GaP wafers are studied by high voltage electron microscopy. Many dislocations are introduced in the epilayer, even if the substrate is nearly dislocation free. The origins of the dislocations in this case are the microdefects, especially the perfect dislocation loops in the substrate. Dislocation dipoles are induced by dis-location half loops appearing at the epi-substrate interface and are classified into three types, two of which are concerned with the interactions of two dipoles in the epilayer, each interaction yielding a screw dislocation segment. The third type of dipole does not extend into the epilayer so far, but terminates and forms an elongated dislocation loop. The interactions and the terminations of dipoles decrease the density of the induced dislocations in proportion to the distances from the interface. The screw dislocations generated by the dipole interactions relax the torsional lattice distortion of the epilayer caused by dopant materials.

Enamine Chemistry—XXIV.: Synthesis, thiation, and reduction of lactams

Enamines, 1, prepared from cyclohexanones or cyclopentanones are reacted with acrylamide to give lactams, the condensed 2-piperidones, 2. Ethyl 2-(1-pyrrolidinyl)-2-cyclohexene-1-propanoate, 3, when treated with primary amines, produces the corresponding N-substituted 2-piperidones, 4. Ethyl 2-(1-pyrrolidinyl)-2-cyclohexene-1-ethanoates and ethyl 2-(1-pyrrolidinyl)-2-cyclopentene-1-ethanoate, 5, react with primary amines to give condensed N-substituted 2-pyrrolidones, 6, and non-cyclic imines, 7. The starting enamines, 1, treated with 2-bromo acetamides only afford the N-alkylated compounds 8 (2-pyrrolidino acetamides), and the regioselectivity of this reaction is rationalized in terms of the HSAB-principle. Compound 1 undergoes an exchange reaction (aminolysis) when reacted with primary amines to give the imines 9. Thiation of the lactams 2 and 6 with the Lawesson reagent (LR), affords the corresponding thiolactams, 10. Reduction of the lactams and thiolactams, 2, 6, and 10 by LAH gives the imines, 11, and the enamines, 16. Further reduction of 11 (LAH) affords the saturated amines, 15. The stereochemistry for the formation of 15 is discussed using the torsion angle notation and the principal of least torsional distortion. In a one-pot reaction using LAH-acetic anhydride the lactams, 2, and the thiolactams, 10, are transformed into the enamides, 14. Compound 14 was also obtained from 11 by direct acetylation with acetic anhydride in the presence of triethylamine.

The influence of torsional vibrations on the molecular configuration determined by gas electron diffraction

As a consequence of intramolecular vibrations distorted apparent structures may result from an electron diffraction analysis of molecules possessing symmetrical equilibrium configuration. The amount of torsional distortion gives information concerning the barrier height to internal rotation. An approach is suggested to estimate barrier heights on the basis of average torsional angles as determined from electron diffraction, and expressions of the rotation-dependent distances as obtained from a Taylor expansion by neglecting higher order terms.

Semiempirical Theory of Excimer Luminescence. II. Comparison with Previous Theories and Consideration of the Transition Probability and the Stability of the Excimer Triplet State

The semiempirical theory of excimer luminescence in the Pariser–Parr–Pople scheme [Paper I, J. Chem. Phys. 48, 2589 (1968)] is shown to be formally equivalent to, but much simpler than, the theories based on the molecular exciton–charge resonance concept. On the basis of an assumption that excimers possess D2h equilibrium conformation, the question of the stability of the excimer triplet state and the thermal distortion of the excimer as the possible source of dipole-allowed character of excimer fluorescence is examined. It is shown that excimer triplet states of many polycyclic hydrocarbons are very likely unstable with respect to dissociation into monomer triplet and monomer ground state, and that thermal excitation of torsional distortion can account for the observed radiative lifetime of excimer fluorescence in naphthalene.

NORMAL MODES, CORIOLIS COUPLING, AND CENTRIFUGAL DISTORTION IN MOLECULES WITH NEARLY FREE INTERNAL ROTATION: CH3—C≡C—CH3 AND CH3—C≡C—SiH3

In 1964 Duncan determined force fields for the molecules CH3—C≡C—CH3 and CH3—C≡C—SiH3 under the assumption that the force constants were not dependent on the torsional angle γ. In the first half of this paper we determine the quantitative effect of adding various γ-dependent force constants to Duncan's force field for CH3—C≡C—CH3. The results lead to complications concerning the symmetry species of the normal coordinates, the magnitude of the Coriolis coupling constants, and the calculation of the energy levels. The possible avoidance of these complications is discussed.In the second half of the paper a formalism is set up relating the rotational and torsional centrifugal distortion constants to the vibrational force field for certain molecules with nearly free internal rotation. Duncan's force field for CH3—C≡C—SiH3 is used to calculate some centrifugal distortion constants for that molecule and for CH3—C≡C—SiD3 on the assumption of completely free internal rotation. Good agreement is obtained between the quantities calculated here and the observed quantities determined by Kirchhoff and Lide.

Hydrogen Bonding of Hydrazoic Acid in Solid Nitrogen

The infrared spectrum of hydrogen bonded HN3 dimers in solid nitrogen has been determined. A dimer band at 387 cm−1, assigned to the torsional distortion of the hydrogen bond, indicates the dimer has an open, not a cyclic structure. The hydrogen bond bending force constant is 0.09 mdyn/Å. The hydrogen bond frequency shift in the N–H stretching mode is 150 cm−1, which, by comparison to similar systems, suggests a hydrogen bond energy of about 2 kcal/mole. The infrared spectrum of monomeric HN3 casts doubt upon the earlier gas-phase assignment of ν6. According to the matrix spectrum, the band center is more likely to be near 588 cm−1.

Electronic Spectrum of (2, 2)Paracyclophane. II

The studies of the absorption and fluorescence spectra of single crystals of (2, 2)paracyclophane in the region 3300–3100 Å reported in a previous paper have been extended. Well-characterized samples with the (hk0) developed crystal plane were used. In absorption two distinct spectra were obtained in the two polarization components. The fluorescence was strongly polarized in one direction (parallel to the fourfold c axis) and represents the mirror image of the equally polarized absorption component. It was concluded that the observations prove conclusively that the differently polarized spectral components represent transitions to two different electronic states, with an energy difference of 369 cm−1. The lowest-energy transition certainly contains the 0–0 line and all available evidence supports the conclusion that also the second transition has allowed character. The only interpretation consistent with all observed features of the spectra is as follows. The two observed states are the gerade dimer states (B2g and B3g in D2h) being the out-of-phase combinations of the B2u and B1u benzene moiety states. The transitions have allowed character due to a torsional distortion of the molecule in the excited state. The interpretation is fully consistent with theoretical energy calculations.

Thermal Buckling of Solid Wings of Arbitrary Aspect Ratio

SUMMARY The thermal buckling of solid wings with all edges free is analyzed by the Rayleigh-Ritz method. First wings of large aspect ratios are treated and the effect is neglected. A double series of orthogonal polynomials is assumed for the de­ flection function, and by the use of successively increasing num­ bers of terms the predominance of the simple torsional distortion is established for a number of typical temperature distributions for wings of constant thickness and of parabolic cross section. The effect of variation of aspect ratio in this analysis is also ex­ amined. The validity of the conclusion about the predominance of the simple torsional distortion is then verified by a buckling analysis for a wing of constant thickness and small aspect ratio, using an approximate solution of the thermal-stress problem of a finite rectangular plate. Having been established as a good approximation, the tor­ sional analysis is now modified to include wings of small aspect ratio also. It is shown that the effects of chordwise normal stresses and shear stresses cancel out, and that the critical tem­ perature of a finite wing can be obtained from that of an infinite wing by multiplication by an end effect factor. This factor is calculated for various temperature distributions for wings of constant thickness, parabolic cross section and double wedge shape, and shown to be approximately the same for different typical temperature distributions and nearly unaffected by the shape of the cross section. The effect is found to be signifi­ cant (more than 10 per cent for aspect ratios below 6), but can be included with very little additional work.