Problem 1 For the truss structure given below, assume A and B are pins, take EA

Question

Problem 1 For the truss structure given below, assume A and B are pins, take EA = 10,000 kips for each member 1) Using only statics, determine the reaction forces at all supports, and draw the axial force diagram for each member of the structure. 2) Using the direct stiffness method, determine the 6 x 6 global stiffness matrix (without boundary condition information), and 2 x 2 global stiffness matrix (with boundary condition information). 3) Use the 2 x 2 global stiffiness matrix, determine the corresponding 2 x 2 flexibility matrix 4) Determine the displacement at each degree of freedom. 5) Determine the reaction forces at all supports 6) Use the member stiffness matrix, determine the axial force in each member. 4 ft 2 kips 3 ft

Explanation / Answer

1)

at joint C

angle

sin= 4/5 ; cos =3/5

at joint C FCA*sin = 2

Or FCA = 2/sin = 2*5/4 = 2.5kips

FCA cos = FB = 2.5*3/5 = 1.5 kips

at node B Vertical reaction VB =0 HORIZONTAL REACTION HB = FCB = 1.5kips (rightward)

at node A VA = FCA*sin = 2 kips (UPWARD)

HA = FCA cos = 1.5 Kips ( leftward )

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