By James F. Doyle (auth.)

This ebook is worried with the static and dynamic research of constructions. Specifi­ cally, it makes use of the stiffness formulated matrix equipment to be used on pcs to take on the various basic difficulties dealing with engineers in structural mechanics. this is often performed by way of masking the Mechanics of constructions, its rephrasing by way of the Matrix equipment, after which their Computational implementation, all inside of a cohesivesetting. even if this e-book is designed basically as a textual content to be used on the upper-undergraduate and starting graduate point, many training structural engineers will locate it worthy as a reference and self-study consultant. a number of dozen books on structural mechanics and as many on matrix tools are presently to be had. A ordinary query to invite is why one other textual content? a wierd devel­ opment has happened in engineering in recent times that may function a backdrop to why this ebook was once written. With the frequent availability and use of comput­ ers, state-of-the-art engineers have on their table tops an research potential undreamt of via earlier generations. even if, the ever expanding caliber and variety of services of commercially on hand software program programs has divided the engineering career into teams: a small staff of expert software writers that be aware of the fine details of the coding, algorithms, and answer thoughts; and a far higher workforce of training engineers who use the courses. it's attainable for this latter team to take advantage of this huge, immense energy with out rather understanding whatever of its source.

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Extra info for Static and Dynamic Analysis of Structures: with An Emphasis on Mechanics and Computer Matrix Methods

Example text

Hence F(x) = -Ft = +F2 This allows easy plotting of the distribution. 7. 8: Displacement and force distributions. 5 Member Distributions and Reaction 31 The displacement distribution is obtained by plotting these four points and connecting them by straight lines. The member force distribution is obtained by first determining the nodal forces. Hence, using the stiffness relation for each member we get [1-1 -1] {O} ~ = {-3} P 1 1 11EA 3 11 EA [1 -1] {I} P L { -3} P L -1 1 4 11EA = 3 11 2EA[ 1 -1]{4} PL {8}P --y- -1 1 0 11EA = -8 11 3EA L These values of nodal force are related to the internal member forces by the previously derived equilibrium conditions.

Assembly with Fixed Boundaries There is an alternative approach that allows the reduced stiffness matrix to be obtained directly. The essential aspect of the approach is to do the reductions before assembling into the structural matrix. The algorithm entails the following steps: Step 1: Determine the size of the structural system. Step 2: Determine the reduced structural system by removing zero degrees of freedom. Step 3: Form the element stiffness matrix. Step 4: Reduce the element stiffness in terms of the non-zero structural degrees of freedom.

The slope, moment and shear force are obtained (in terms of the nodal degrees of freedom) simply by differentiation. 7) Therefore, the nodal moments are easily related to the nodal degrees of freedom. By carrying out the indicated differentiations we can also relate the nodal forces to the nodal degrees of freedom. 2 Beam Element Stiffness Matrix the element nodal loads vector and the corresponding nodal displacements vector as the following column matrices {F}: iE: } and {u}: {~d respectively.

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