Advanced Methods of Structural Analysis

6.4 Displacement Due to Settlement of Supports and Errors ofFabrication 175 However,XD 1 , and therefore the required displaceme ...

176 6 Deflections of Elastic Structures It is obvious that the effect of geometric incompatibility may be useful for regulation ...

6.5 Graph Multiplication Method 177 is obvious that in theunit statethe bending moment diagramMN is always bounded by thestraigh ...

178 6 Deflections of Elastic Structures d W 1 W 2 Mp y 1 y (^2) M W 1 W 2 W (^3) y 1 y 2 y 3 M Mp e W 2 y 1 W 1 M y 2 Mp a b l/2 ...

6.5 Graph Multiplication Method 179 Sometimes it is convenient to subdivide the curved bending moment diagram by a number of “go ...

180 6 Deflections of Elastic Structures Fig. 6.21 (a) Actual state, unit state forAand corresponding bending moment diagrams. ( ...

6.5 Graph Multiplication Method 181 Ta b l e 6. 5 Graph multiplication procedures Displacement General formula (6.20) D 1 EI ̋y ...

182 6 Deflections of Elastic Structures Fig. 6.22 Design diagram of the beam and bending moment diagrams for actual and unit sta ...

6.5 Graph Multiplication Method 183 a EI 1 EI 3 EI 2 l P h A B CD Design diagram Unit state for Dhor A B 1 ⋅h 1 ⋅h M H = 1 P^ =1 ...

184 6 Deflections of Elastic Structures moment diagrams is located one under the other and vertical portionACis located one besi ...

6.6 Elastic Loads Method 185 Discussion.In actual state, the bending moment along the right vertical bar does not arise; as a re ...

186 6 Deflections of Elastic Structures Fig. 6.24 Unitstate for calculation of elastic load at jointn n dn– 1 dn Fn–1 =1/dn–1 Fn ...

6.6 Elastic Loads Method 187 are zero, the members with nonzero internal forces are located within only two panels of the truss, ...

188 6 Deflections of Elastic Structures Elastic loadW 3 Two unit couples are applied to members 2-3 and 3-4. Performing similar ...

6.7 Reciprocal Theorems 189 Summary The elastic load method is based on conjugate beam method. According to this method, displac ...

190 6 Deflections of Elastic Structures P 1 D 11 D 21 D 11 D 22 D 22 D 11 D 21 D 12 D 1 D 2 D 12 D 12 D 22 State 1 State 2 A 1 P ...

6.7 Reciprocal Theorems 191 denoted by letterımn. The first indexmindicates the direction of the displacement and the second ind ...

192 6 Deflections of Elastic Structures 6.7.3 Theorem of Reciprocal Unit Reactions (Rayleigh First Theorem) Let us consider two ...

6.7 Reciprocal Theorems 193 6.7.4 Theorem of Reciprocal Unit Displacements and Reactions (Rayleigh Second Theorem) Let us consid ...

194 6 Deflections of Elastic Structures Computation of displacements Initial parameters method n! F(x − aF)n Fictitious beam met ...