Advanced Methods of Structural Analysis

6.2 Initial Parameters Method 155 Thus, displacement at pointBequals EIy.l/D  RA P 2  l^3 2  RAl^3 6 C P 6  l 2  3 : (e) 2 ...

156 6 Deflections of Elastic Structures This equation contains the unknown initial parameter 0 and two unknown reactions RAandR ...

6.2 Initial Parameters Method 157 Fig. 6.7 Fixed-rolled beam subjected to the angular settlementof support q 0 l y MA RA qx^0 y( ...

158 6 Deflections of Elastic Structures Fig. 6.8 Fixed-fixed beam subjected to linear settlement of support RB B DB RA MB MA l A ...

6.3 Maxwell–Mohr Method 159 6.3 Maxwell–Mohr Method The Maxwell–Mohr procedure presents a universal method for computation of di ...

160 6 Deflections of Elastic Structures Both expressions present thelinearfunctions of the loadsPandM. In general case, suppose ...

6.3 Maxwell–Mohr Method 161 P-condition; andMNk,NNk,QNkare the internal stresses due to the unit load, which acts in thekth dire ...

162 6 Deflections of Elastic Structures (c)For mutual linear displacement of twosections, a corresponding dummy load represents ...

6.3 Maxwell–Mohr Method 163 (b)The vertical displacement atAmay be calculated by formula yAD 1 EI Zl 0 Mp.x/MNdx; (c) where expr ...

164 6 Deflections of Elastic Structures Actual state. Reaction of supportsRADRBDP. As usual, the axial forces in the members are ...

6.3 Maxwell–Mohr Method 165 Ta b l e 6. 3 Calculation of vertical displacement of the joint 6 of the truss Length of the bar (m) ...

166 6 Deflections of Elastic Structures section of the member ish 0. The upper and bottom fibers of the member are subjected to ...

6.3 Maxwell–Mohr Method 167 with neutral axis). If the cross section is nonsymmetrical about its neutral axis, then the term.t 1 ...

168 6 Deflections of Elastic Structures Solution.Since the required displacement isC, then a structure in the unit state is loa ...

6.3 Maxwell–Mohr Method 169 a R R R A B C +t 1 +t 2 DB h 0 b x X=1 x R y j R y ds A B HA C +t 1 +t 2 DB dj Fig. 6.14 Curvilinear ...

170 6 Deflections of Elastic Structures 6.3.3 Summary 1.Maxwell–Mohr integral presents the fundamental and power method for calc ...

6.4 Displacement Due to Settlement of Supports and Errors ofFabrication 171 According to this principle, the elementary work don ...

172 6 Deflections of Elastic Structures Ta b l e 6. 4 Determination of displacements due to se ttlements o f support Displacemen ...

6.4 Displacement Due to Settlement of Supports and Errors ofFabrication 173 Actual state A¢ C B A K 5m 3m 4m 6m 2m Δ 1 q Δ Δ 2 a ...

174 6 Deflections of Elastic Structures In fact the formula (c) is expression (6.18) in the expanded form. The required horizont ...