Question

Statics problems

Question A2 The plane truss shown in Figure A2 is supported at points A and J. -30° and the external loads are Fi 1.5 kN and F 3 kN. Draw the free body diagram of the truss. Determine all the reactions at the supports or, if this is not possible, explain why. a) Calculate the internal forces in members CF, EH, GH and HI, stating whether they are in tension or compression. b) (12) Are members CF and HG in the ideal orientation or should they be moved to positions DE and EI, respectively? Clearly justify your c) 2 m 2 m Fi F2 2 m 2 m 2 m 2 m Figure A2. Question A2 The plane truss shown in figure A2 is supported at points A and G. Neglecting the self-weight of the structure: Draw the free body diagram of the truss and determine all the reactions at the supports. b) Determine the internal forces in members DE, EI, FI and HI, stating whether they are in tension or compression. (16) 3P 2P 2P 3 tm 4 m 14 m Figure A2

Answer 1

A2)

a) The FBD of the truss is as shown below:

Ay Ax A 2 m 3sin30 1.5 F2 3cos30 2 m Figure A2

Applying COE,

$\Sigma M_A = 0$

-1.5 x 2 + 3 sin 30 x 2 - 3 cos30 x 6 + Jx * 4 = 0

Jx = 3.9 kN

$\Sigma F_y = 0$

Ay - 1.5 - 3cos30 = 0

Ay = 4.1 kN

$\Sigma F_x = 0$

-Ax + 3 sin30 + 3.9 = 0

Ax = 5.4 kN

b)

Consider a section of the truss as shown

D Fdf Fcf sin45 4.1 15.4 A Fce In Fi

$\Sigma F_y = 0$

4.1 FCE. * S27245 0

FeF =-5.8 kN, (cornpression)

Now consider a section as shown;

sin45 T Fgi 3sin 30 F2 3 cos30 3.9 im in

$\Sigma F_x = 0$

FCH * cos45 +3 sin30+3.90

FGH7.64 kN (compression)

$\Sigma M_I= 0$

FGH * sin45 * 2 FEH * 2-3.9 *2=0

FEH 6.6 kN (Tension)

now consider joint H

Fgh Feh Fgh sin45 Fgh cos45

$\Sigma F_x = 0$

FHI = 5.4 kN (Tension)

c) The orientation of the diagonal members should be such that the longest members are subject to tension and the shorter ones are in compression. Here as the members CF and GH are both in compression, it might be advantageous to move them to the suggested position of DE and EI. This way, they can be in tension and it might be possible to reduce the material in their design , thereby producing an efficient design