Test: Trusses -2 - Civil Engineering (CE) MCQ

At join D, the equilibrium shows the force in member CD is 50 kN tensile.

For plane truss assumptions are:
(i) Weight of all members are neglected. All members are straight.
(ii) All connections are smooth, frictionless pins.
(iii) External loads are applied directly to the pin joints.
(iv) All frames are perfect, hence statically determinate.

Cutting a section through members CA, CD, DEand EB and taking moment of the upper part about E.

∴ F_ca x 6 + 10 x 6 - 20 x 3 = 0
∴ F_ca = 0

Force in AB or AC [Consider joint B],

So in case I force in members will be less than that in case II.
From symmetry, there will be only vertical deflection of joint B.

• Zero-force member conditions:

  • If two non-collinear members meet at a joint with no external load or support, both are zero-force members.
  • If three members form a truss joint where two are collinear and no load or support is applied, the non-collinear member has zero force.

• Applying conditions:

  • Identify such joints in the truss diagram.
  • Based on the geometry, 7 members meet the criteria.

Step-by-Step Application:

1. Left Triangle (Top Joint):

   • Top joint has no external load or support.
   • Two non-collinear members meet here:
     • The diagonal member is zero-force (1 member).

2. Middle Left Triangle (Top Joint):

   • Similar condition as above. Top joint has no load or support.
   • The diagonal member is zero-force (2nd member).

3. Middle Right Triangle (Top Joint):

   • Again, top joint with no load or support.
   • The diagonal member is zero-force (3rd member).

4. Right Triangle (Top Joint):

   • Same condition applies as the left triangle.
   • The diagonal member is zero-force (4th member).

5. Horizontal Members (Middle):

   • Horizontal members at the middle of triangles connect unloaded joints.
   • These members are zero-force due to symmetry:
     • Two horizontal members are zero-force (5th and 6th members).

6. Diagonal Member (Bottom Middle Joint):

   • The diagonal member connecting the bottom middle joint is zero-force (7th member).

Final Count:

• Total 7 zero-force members identified based on the above conditions.

Correct Answer: (c) 7.

At joint C there is no external force so force in member BC is zero.