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The capacity of a single ISA 100 x 100 x 10 mm as tension member connected by one leg only using 6 rivets of 20 mm diameter is
The allowable stress is 150 N/mm2
- a)333 kN
- b)253 kN
- c)238 kN
- d)210 kN
Correct answer is option 'D'. Can you explain this answer?
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The capacity of a single ISA 100 x 100 x 10 mm as tension member conne...
The net area of the tension member is given by,
The angle section is connected by one leg only.
The angle section is connected by one leg only.
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The capacity of a single ISA 100 x 100 x 10 mm as tension member conne...
Calculation of Capacity of Tension Member Connected by One Leg Only
Given data:
Cross-sectional area (A) of single ISA = 100 x 100 mm
Thickness (t) of single ISA = 10 mm
Diameter (d) of one rivet = 20 mm
Number of rivets (n) = 6
Allowable stress (σallow) = 150 N/mm2
1. Calculation of Net Area (Anet)
The net area of the cross-section after deducting the area of the rivet holes can be calculated as follows:
Area of one rivet hole = π/4 x d2 = π/4 x 202 = 314.16 mm2
Area of six rivet holes = 314.16 x 6 = 1884.96 mm2
Net area (Anet) = A - Area of six rivet holes
Anet = 100 x 100 - 1884.96
Anet = 8115.04 mm2
2. Calculation of Ultimate Load (Pult)
The ultimate load that can be carried by the tension member can be calculated as follows:
Ultimate shear strength of one rivet (Pus) = 0.8 x π/4 x d2 x σallow
Pus = 0.8 x π/4 x 202 x 150
Pus = 9426 N
Ultimate load carried by one rivet (Pur) = Pus x d
Pur = 9426 x 20
Pur = 188520 N
Ultimate load carried by six rivets (Pult) = Pur x n
Pult = 188520 x 6
Pult = 1131120 N
3. Calculation of Capacity of Tension Member (Pcap)
The capacity of the tension member connected by one leg only can be calculated as follows:
Capacity of tension member (Pcap) = 0.75 x Anet x σallow
Pcap = 0.75 x 8115.04 x 150
Pcap = 915352.4 N
4. Comparison of Pult and Pcap
The capacity of the tension member calculated from the net area and allowable stress is less than the ultimate load that can be carried by the six rivets. Hence, the capacity of the tension member is limited by the strength of the rivets.
Final Answer: The capacity of a single ISA 100 x 100 x 10 mm tension member connected by one leg only using 6 rivets of 20 mm diameter is 210 kN.
Given data:
Cross-sectional area (A) of single ISA = 100 x 100 mm
Thickness (t) of single ISA = 10 mm
Diameter (d) of one rivet = 20 mm
Number of rivets (n) = 6
Allowable stress (σallow) = 150 N/mm2
1. Calculation of Net Area (Anet)
The net area of the cross-section after deducting the area of the rivet holes can be calculated as follows:
Area of one rivet hole = π/4 x d2 = π/4 x 202 = 314.16 mm2
Area of six rivet holes = 314.16 x 6 = 1884.96 mm2
Net area (Anet) = A - Area of six rivet holes
Anet = 100 x 100 - 1884.96
Anet = 8115.04 mm2
2. Calculation of Ultimate Load (Pult)
The ultimate load that can be carried by the tension member can be calculated as follows:
Ultimate shear strength of one rivet (Pus) = 0.8 x π/4 x d2 x σallow
Pus = 0.8 x π/4 x 202 x 150
Pus = 9426 N
Ultimate load carried by one rivet (Pur) = Pus x d
Pur = 9426 x 20
Pur = 188520 N
Ultimate load carried by six rivets (Pult) = Pur x n
Pult = 188520 x 6
Pult = 1131120 N
3. Calculation of Capacity of Tension Member (Pcap)
The capacity of the tension member connected by one leg only can be calculated as follows:
Capacity of tension member (Pcap) = 0.75 x Anet x σallow
Pcap = 0.75 x 8115.04 x 150
Pcap = 915352.4 N
4. Comparison of Pult and Pcap
The capacity of the tension member calculated from the net area and allowable stress is less than the ultimate load that can be carried by the six rivets. Hence, the capacity of the tension member is limited by the strength of the rivets.
Final Answer: The capacity of a single ISA 100 x 100 x 10 mm tension member connected by one leg only using 6 rivets of 20 mm diameter is 210 kN.
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The capacity of a single ISA 100 x 100 x 10 mm as tension member connected by one leg only using 6 rivets of 20 mm diameter isThe allowable stress is 150 N/mm2a)333 kNb)253 kNc)238 kNd)210 kNCorrect answer is option 'D'. Can you explain this answer?
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