Two equal angles ISA 100 mm × 100 mm of thickness 10 mm are place
Two equal angles ISA 100 mm × 100 mm of thickness 10 mm are placed back to back and connected to either side of a gusset plate through a single row of 16 mm diameter rivets in double shear. The effective areas of the connected and unconnected legs of each of these angles are 775 mm2 and 950 mm2, respectively.
A. If these angles are tack riveted the net effective area of this pair of angles is 1725 mm<sup>2</sup>
B. If these angles are not tack riveted the net effective area of this pair of angles is 2899 mm<sup>2</sup>
C. If these angles are tack riveted the net effective area of this pair of angles is 3450 mm<sup>2</sup>
D. If these angles are not tack riveted the net effective area of this pair of angles is 1449.5 mm<sup>2</sup>
Please scroll down to see the correct answer and solution guide.
Right Answer is:
SOLUTION
Concept
1. If 2 angles placed back to back and connected to gusset plate on same side.
\(\begin{array}{l} {A_{net}} = {A_1} + K{A_2}\\ K = \left( {\frac{{5{A_1}}}{{5{A_1} + {A_2}}}} \right) \end{array}\)
Note: If tack rives not provided, each angle will behave independently and \(K = \frac{{3{A_1}}}{{3{A_1} + {A_2}}}\)
2. If two angles are placed back to back and connected to gusset plate on both sides.
\({A_{net}} = {A_1} + {A_2}\) [if tack riveted ]
\({A_{net}} = {A_1} + K{A_2}\) [not tack riveted]
\(K = \left( {\frac{{3{A_1}}}{{3{A_1} + {A_2}}}} \right)\)
Calculation
Given,
Area of connected leg (A1) = 775 mm2, Area of unconnected leg (A2) = 950 mm2
i) If legs are tack riveted
Anet = A1 + A2
Anet = 775 + 950 = 1725 mm2
Since, 2 Angles are connected
Total Area of both the angles = 2 × 1725
= 3450 mm2
ii) When legs are not tack riveted
Anet = A1 + k × A2
where, \(k = \left( {\frac{{3{A_1}}}{{3{A_1} + {A_2}}}} \right)\)
\(k = \left( {\frac{{3×{775}}}{{3{×775} + {950}}}} \right)\)
= 0.71
Anet = 775 + 0.71 × 950 = 1449.5 mm2
Since two angles are connected
Equivalent area = 2 × 1449.5 = 2899 mm2
