The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are

The correct answer is BF and DH only.

Step-by-Step Explanation:

To identify the zero-force members in the given truss, we can use the method of joints and apply the standard rules for identifying zero-force members:

Rule for Three-Member Joints:
If three members meet at a joint where no external load or support reaction is applied, and two of the members are collinear (lying along the same straight line), then the third non-collinear member must carry zero force.

Let's analyze the joints of interest from the truss shown in the image:

1. Analysis at Joint B:
Joint B is located along the bottom chord, positioned 1 m from support A. The members connected to joint B are AB, BC, and BF.
- Members AB and BC are collinear along the horizontal direction.
- Member BF is a vertical member (non-collinear).
- There is no external load or support reaction acting at joint B.
By setting up the equilibrium equation in the vertical (y) direction at joint B:

$\sum F_y=0\Rightarrow F_{\text{BF}}=0$

Therefore, BF is a zero-force member.

2. Analysis at Joint D:
Joint D is located along the bottom chord, positioned 1 m from support E. The members connected to joint D are CD, DE, and DH.
- Members CD and DE are collinear along the horizontal direction.
- Member DH is a vertical member (non-collinear).
- There is no external load or support reaction acting at joint D.
By setting up the equilibrium equation in the vertical (y) direction at joint D:

$\sum F_y=0\Rightarrow F_{\text{DH}}=0$

Therefore, DH is a zero-force member.

Consequently, the members carrying zero force are BF and DH only.