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Related Concept Videos

Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

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Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
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Unsymmetric Bending - Angle of Neutral Axis01:15

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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Singularity Functions for Bending Moment01:18

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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Castigliano's Theorem01:18

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Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
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Boundary Conditions: Lossless Lines01:21

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Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
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The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
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Bi-alignments with affine gaps costs.

Peter F Stadler1,2,3,4,5,6, Sebastian Will7

  • 1Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstraße 16-18, 04107, Leipzig, Germany. studla@bioinf.uni-leipzig.de.

Algorithms for Molecular Biology : AMB
|May 16, 2022
PubMed
Summary
This summary is machine-generated.

Bi-alignments model incongruent evolution of protein sequences and structures. This new algorithm efficiently computes optimal alignments, revealing sequence-structure shifts.

Keywords:
Dynamic programmingMulti-tape formal grammarRecursionScoring functions

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Area of Science:

  • Computational biology
  • Bioinformatics
  • Structural biology

Background:

  • Traditional sequence and structure alignments assume congruent evolution.
  • Incongruent evolution, where sequence and structure diverge positionally, requires new alignment methods.
  • Bi-alignments generalize sequence and structure alignments to model incongruent evolution.

Purpose of the Study:

  • To introduce and describe the computational framework for bi-alignments.
  • To present an efficient algorithm for computing optimal bi-alignments with affine gap costs.
  • To enable the study of relative shifts between protein sequences and structures.

Main Methods:

  • Developed a novel bi-alignment framework generalizing pairwise sequence and structure alignments.
  • Implemented an exact algorithm for optimal bi-alignments with affine gap costs in quartic space and time.
  • Extended the algorithm to handle affine shift and sub-additive gap costs for efficient optimization.

Main Results:

  • Optimal bi-alignments with affine gap costs can be computed exactly.
  • Efficient computation of bi-alignments with affine shift and sub-additive gap costs is achievable.
  • The affine cost bi-alignment algorithm is capable of handling large proteins.

Conclusions:

  • Affine cost bi-alignments offer a practical approach to analyzing sequence-structure relationships.
  • This method is valuable for studying shifts and divergences in protein evolution.
  • The algorithm is publicly available for use in biological research.