In-plane forces

A plate buckles when the in-plane compressive load gets so large that the originally flat equilibrium state is no longer stable, and the plate deflects into a nonflat (wavy) configuration. The load at which the departure from the flat state takes place is called the buckling load. The flat equilibrium state has only in-plane forces and undergoes only ex-... 

From Figure D-5 for in-plane forces, force equilibrium in the x-direction yields... 

From moment equiiibrium about the x-axis to which the moments of Figure D-7 and the lateral forces of Figure D-6 contribute (but not the in-plane forces of Figure D-5 because they are either parallel to or perpendicular to the x-axis),... 

Sugawara, Y., A. Y. Hirakawa, and M. Tsuboi. 1984. In-Plane Force Constants of the Peptide Group Least-Squares Adjustment Starting from Ab Initio Values of N-Methylacetamide. J. Mol. Spectrosc. 108, 206-214. 

The side walls are defined relative to the explosion source as shown in Figure 3.6. These walls will experience less blast loading than the front wall, due to lack of overpressure reflection and to attenuation of the blast wave with distance from the explosion source. In certain cases, the actual side wall loading is combined with other blast induced forces (such as in-plane forces for exterior shear walls). The general form of side wall blast loading is shown in-Figure 3.8,... 

We may draw the following conclusions at this point. Forces on nuclei are determined not only by the atomic charges, but include terms from the charge flux. As can be seen from the example of water, it appears that the charge flux may be fairly significant. In water, the neglect of charge flux causes an 80% error in the in-plane forces. Additional research is under way to further characterize these effects and their importance. 

The out-of-plane equilibrium of a plate subject to in-plane forces Nx, Ny and Nxy which give rise to buckling instability is defined by... 

From Equation (4.43) it is seen that the in-plane stress resultants for a laminated plate are not only a function of the mid-surface strains, as in a homogeneous plate, but are also in general a function of the curvature and twisting tautology. Stated in another way, in-plane forces can cause curvatures of the plate, and there is also an interplay between twisting and normal effects. 

In-plane forces and bending moments per unit length... 

The in-plane forces or membrane forces and bending moments per unit length, depicted in Fig. 11.39, are defined as through-thickness integrals of planar stresses, assuming that the laminate consists of perfectly bonded laminae or layers. 

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