Aerospace Structures (c) Eric Raymond Johnson. CC BY NC SA https://doi.or g/10.21061/AerospaceStructures 437 CHAPTER 16 Applications of the direct stiffness method 16.1 Coplanar trusses The member stiffness matrix for a truss bar in the X-Y plane is developed from the analysis in article 6.1.1 on page 153. A typical bar of length located between joints i and j is shown in figure. 16.1. The coordinates of beginning joint i are , and coordinates of the end joint j are , in the undeformed state. The angle between the positive X-direction and directed line element i-j is denoted as , and is determined from . (16.1) The axial force N i-j from eq. (6.2) on page 154 is . (16.2) The elongation is related to the joint displacements by eq. (6.6) on page 155, which is repeated as (16.3) L X i Y i , ( ) X j Y j , ( ) θ θ cos ( ) i j – X j X i – L i j – --------------- = θ sin ( ) i j – Y j Y i – L i j – -------------- = L i j – X j X i – ( ) 2 Y j Y i – ( ) 2 + = θ θ N i j – N i j – EA L ------- i j – q 2 i 1 – Q 2 i 1 – , q 2 i Q 2 i , i q 2 j 1 – Q 2 j 1 – , q 2 j Q 2 j , j X Y Fig. 16.1 Truss bar connected to joints i and j. N i j – EA L ------- i j – ∆ i j = N T ( ) i j – – = ∆ i j –
Applications of the direct stiffness method
Jun 21, 2023
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