Normal Bending Moment Research Articles

Finite Deflections of Curved Beams

A theory was developed to predict load-deflection curves for curved beams under loading conditions that produce finite strains. The theory assumed that the curved beam could be approximated by a number of truncated pie-shaped segments with circular arcs for the inner and outer boundaries. The cross section of each segment was assumed to have a plane of symmetry; the centroidal normal force and bending moment acting on the segment were assumed to lie in the plane of symmetry and to remain constant over the included angle of the segment. Using known tension and compression engineering stress-strain diagrams, internal values of centroidal normal force and moment could be calculated for assumed deformations of the segment. An iterative procedure was used to obtain the deformations which would make the internal values of centroidal normal force and moment equal to the applied values. The deformed shapes of the pie-shaped segments were reassembled to give the deformed shape of the curved beam. Good agreement was found between theory and experiment for nine mild steel curved beams and two commercially available crane hooks.

Some General Considerations on the Natural Mode Technique

We continue our fundamental discourse on the natural modes in an element and extend our considerations to large displacements. First, we present a general procedure for establishing the so-called geometrical stiffness kG, when the natural modes of the complete element are given. The theory is a substantial generalisation and clarification of the method initially given in refs. 2 and 3 and shows that in establishing the modification to the transformation matrix aN it is necessary to ignore the contribution of the natural modes, which cause rotation at the nodal points but no displacement there. The point is subtle and was not made in ref. 2, although the applications given there are correct. As an example, the geometrical stiffness of a straight beam in space with all degrees of freedom is established. There follows the extension of the geometrical stiffness concept to a sub-element. This is of great practical significance for two reasons. First, it allows to derive the geometrical stiffness of elements of complex shape and behaviour, e.g. curved beams in space subjected to normal forces, bending moments and torque.

The yield criterion for orthotropically reinforced concrete slabs

The yield criterion for orthotropically reinforced concrete slabs, usually defined in terms of the normal bending moment and twisting moment on a yield line, is shown to be essentially an envelope of permissible normal bending moments. The yield criterion is shown to be of hyperbolic form when expressed in terms of principal moments and the associated flow rule to be consistent with the plastic potential theory. The conditions to be satisfied at the intersections of yield lines with each other and with free edges, to obtain statically admissible moments are examined.

弾塑性域における軸方向力をうけるH型断面部材の研究

The deformation of wide flange sections subjected to a normal compressive force and bending moments in the elasto plastic range is studied with an assumption that the flange is concentrated in its gravity centre. An illustrative result obtained through a numerical integration by a computer is given in two charts, which may be correspond to the modified slope deflection coefficients. Then the effects of the cross sectional shape and of the yield strength in materials are discussed with those coefficients. Finally the design criterion of columns unrestricted to side sway is roughly estimated with elasto-plastic deformation characteristics and is compared with the AISC design formula for the plastic design. It may be found that there is afair coincidence between those criteria.

Analysis of Prestressed Cylindrical Shell Roofs

Circular cylindrical shell roofs prestressed by tendons placed in edge beams are considered. Prestressing force is represented by a Fourier series and several terms of the series are taken into account. For the solution of edge disturbance problem, Schorer approximation is used. The solution is facilitated by operation tables referring to a single shell and an inner shell in multiple shell structure. Two numerical examples are given. It is demonstrated that extremal values of normal stresses and transverse bending moments do not occur at midspan, but are rather displaced in the direction of the end section.