"The age group of the children studied typically experience major changes in body type and body mass index, and the sample does not represent a valid cross section of the American population".
But that's not nearly good enough for a survey designed to reflect a scientifically valid cross section of the country, he says.
This raises questions about whether the participants represent a valid cross section of public opinion.
For a fixed C, our procedure provides a 'nonparametric analysis of covariance', which is valid for cross-section or panel data.
Additionally, the plate height depends on a dimensionless geometrical factor, for which an expression is obtained to be valid for arbitrary cross-section geometry.
And two modified slenderness parameters are identified which enables the result to be valid for any symmetric cross-section shape.
This two-part contribution presents a beam theory with a non-uniform warping including the effects of torsion and shear forces, and valid for any homogeneous cross-section made of isotropic elastic material.
This two-part contribution presents a beam theory (BT) with a non-uniform warping (NUW) including the effects of torsion, and shear forces and valid for any homogeneous cross-section made of isotropic elastic material.
We present general analytical expressions of the effective stiffness coefficients, valid for beams of arbitrary cross-section shape.
The expression is valid for any shape of cross-section, subjected to combined axial loads and biaxial bending, both for short-time and sustained loads, normal and high strength concretes, but it is only suitable for columns with equal effective buckling lengths in the two principal bending planes.
But, as long as it exceeds sufficiently the cross-section, it is valid except for very low values of ( varepsilon_{text{L}} )/yL that correspond to a very low premature elastic stress state, which usually are not of interest.
