By Saouma V.E.
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Additional resources for Lecture Notes in Structural Engineering: Analysis and Desig
2 where the vertical load is per unit horizontal projection (such as an external load but not a self-weight). Due to symmetry, the vertical reaction is simply V = wL 2 , and there is no shear across the midspan of the arch (nor a moment). , and H is analogous to the C − T forces in a beam, and h is the overall height of the arch, Since h is much larger than d, H will be much smaller than C − T in a beam. Since equilibrium requires H to remain constant across thee arch, a parabolic curve would theoretically result in no moment on the arch section.
5 1 More about this in Matrix Structural Analysis. 2 Internal Work Considering an infinitesimal element from an arbitrary structure subjected to uniaxial state of stress, the strain energy can be determined with reference to Fig. 2. The net force acting on the element while deformation is taking place is P = σx dydz. The element will undergo a displacement u = εx dx. Thus, for a linear elastic system, the strain energy density is dU = 12 σε. 3 175 Virtual Work 11 A severe limitation of the method of real work is that only deflection along the externally applied load can be determined.
4 Examples 221 3. In the following discussion the contributions to displacements due to axial strain are denoted with a single prime ( ) and those due to curvature by a double prime ( ). 4. Consider the axial strain first. A unit length of frame member shortens as a result of the temperature decrease from 85◦ F to 45◦ F at the middepth of the member. 56) 5. The effect of axial strain on the relative displacements needs little analysis. 0044 ft. The shortening of the vertical members results in no relative displacement in the vertical direction 2.
Lecture Notes in Structural Engineering: Analysis and Desig by Saouma V.E.