《结构工程中的数学方法》课程教学课件（讲稿）intro_system_structure

2AlgebraicproblemsinmatrixformSystems of Linear EquationsSystem structure-introductory exampleeguationsof eguilibriumforaframe+X2=AyOZM.=0:AyAb2a·x, +b·x, =x2=AX1OZM=O:rDb24qaaX+bx,qo22525UCZF =0:S0bB3= B-b.qOX35bCsysteminmatrixformb0b00.5.b2.qa0.5.b2abA=0.5.ab0.5.a-0.4.a-0.4.a0.5.b2.q0.5.b2.0-100.6-10.6-b.q-b.qX33aMichael Beer,Engineering Mathematics

Michael Beer, Engineering Mathematics equations of equilibrium for a frame Systems of Linear Equations System structure − introductory example 2 Algebraic problems in matrix form 33a b c 0.75 c a A B C q x y x1 = Ax x2 = Ay x3 = B 0.5 a D q b a A C ∑M 0: C = 2 1 2 b ax bx q 2 ⋅ +⋅ = ⋅ + + ∑M 0: D = 2 12 3 a a4 b x bx x q 2 25 2 ⋅ +⋅ − ⋅ ⋅ = ⋅ + ∑F 0: y = 2 3 3 x x bq 5 − + ⋅ =− ⋅ system in matrix form ● ● 2 1 2 2 3 a b 0 x 0.5 b q 0.5 a b 0.4 a x 0.5 b q 0 1 0.6 x b q      ⋅ ⋅      ⋅ − ⋅⋅ = ⋅⋅       −     − ⋅      2 2 a b 0 0.5 b q , 0.5 a b 0.4 a 0.5 b q ˆ 0 1 0.6 b q   ⋅ ⋅   = ⋅ − ⋅ ⋅⋅ − − ⋅   A