The problem asks us to determine the degree of static indeterminacy of a rigid plane frame. We need to find the number of members, reactions, and joints in the frame.

1. Problem Description

The problem asks us to determine the degree of static indeterminacy of a rigid plane frame. We need to find the number of members, reactions, and joints in the frame.

2. Solution Steps

Step 1: Count the number of members ($m$).

The frame has 4 columns and 4 horizontal beams in each bay, with 3 bays. So, there are $4 \times 3 = 12$ vertical members and $4 \times 3 = 12$ horizontal members. Hence, $m = 12 + 12 = 24$.

Step 2: Count the number of reactions ($r$).

There are two fixed supports and one hinged support. Each fixed support provides 3 reactions (vertical, horizontal, and moment), and the hinged support provides 2 reactions (vertical and horizontal).

Therefore, the total number of reactions is $r = (2 \times 3) + 2 = 6 + 2 = 8$.

Step 3: Count the number of joints ($j$).

There are 4 levels with 4 joints each and in total 12 columns and 12 horizontal beams. Hence there are 12 joints.

Step 4: Calculate the degree of static indeterminacy ($D_s$).

For a rigid plane frame, the degree of static indeterminacy is given by:

$D_s = 3m + r - 3j$

Substitute the values:

$D_s = 3(24) + 8 - 3(12)$

$D_s = 72 + 8 - 36$

$D_s = 80 - 36$

$D_s = 44$

3. Final Answer

The degree of static indeterminacy is 44.