=有4.n, 417 Thus the disp =(-÷n(-￥州 医附图…俗会… FLEXURE ELEMENT WITHAXIAL LOADING FLEXURE ELEMENT WITH AXIAL LOADING m 清运 陶-巴 3 3 Application of boundary conditions: The coefficients obtained: Thus the displacement function expressed in form of nodal variables: In interpolation form: In matrix form: Introducing dimensionless coordinates: the normal stress distribution on a cross section located at axial position x: For the FLEXURE ELEMENT STIFFNESS MATRIX, Please refer to textbook for the details. FLEXURE ELEMENT WITH AXIAL LOADING (a) Beam with bending moment and axial load. (b) Section of beam, illustrating how tensile load reduces bending moment, hence, “stiffening” the beam. It must be pointed out that there are many ramifications to this seemingly simple extension. If the axial load is compressive, the element could buckle. If the axial load is tensile and significantly large, a phenomenon known as stress stiffening can occur. As shown in Figure b, in a beam subjected to both transverse and axial loading, the effect of the axial load on bending is directly related to deflection, since the deflection at a specific point becomes the moment arm for the axial load. In cases of small elastic deflection, the additional bending moment attributable to the axial loading is negligible. FLEXURE ELEMENT WITH AXIAL LOADING simply add the spar element stiffness matrix to the flexure element stiffness matrix to obtain the 6 × 6 element stiffness matrix for a flexure element with axial loading as a non-coupled superposition of axial and bending stiffness