--- title: "Shear stress in rivets B and C" subject: "Design of Steel and Timber Structure" chapter: 4 key: "semester_6/design_of_steel_and_timber_structure:rivet-shear-stress-b-c" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/rivet-shear-stress-b-c site: BCT Engineering --- # Shear stress in rivets B and C Design of Steel and Timber Structure · Chapter 4: Connections in Steel Structures - Asked in: 2068 Magh (old course), 14 marks - Video: [Stresses on riveted plates](https://www.youtube.com/watch?v=9NwUmCmQbFU) — MathiBae - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/rivet-shear-stress-b-c - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-4 ## Question Calculate the shear stress in the rivet B and C for the connection shown in figure below. Rivets A and B have 16mm diameter while C has a diameter of 20mm. [Figure: bracket plate with rivets A and B placed 60 mm above and 60 mm below the horizontal axis at 90 mm from the load line, rivet C on the axis; 20 kN load acts at 120 mm from the vertical line of rivet C] ## Short answer Shear stress in rivet B is about 74.5 N/mm², in rivet C about 5.3 N/mm². ## Answer **Working stress method (IS 800:1984).** Hole diameters are used for the rivet areas: $d_0=d+1.5$ mm, i.e. 17.5 mm for the 16 mm rivets (A, B) and 21.5 mm for the 20 mm rivet (C). **Reading of the figure:** rivets A and B are 60 mm above and below the horizontal axis and 90 mm from the load line; rivet C is on the axis, 120 mm from the load line. $P=20$ kN, vertical. #### Step 1 - rivet areas and centroid of the group - $A_A=A_B=\dfrac{\pi}{4}(17.5)^2=240.5$ mm²; $A_C=\dfrac{\pi}{4}(21.5)^2=363.1$ mm²; $\Sigma A=844.1$ mm² - Distance of centroid from load line: $\bar x=\dfrac{2A_A(90)+A_C(120)}{\Sigma A}=102.90$ mm - So A, B are $12.90$ mm on the load side of the centroid and C is $17.10$ mm on the far side. #### Step 2 - direct shear stress (same in all rivets) $\tau_d=\dfrac{P}{\Sigma A}=\dfrac{20000}{844.1}=23.69$ N/mm² (vertical) #### Step 3 - torsion $M=Pe=20\times10^3\times102.90=2058\times10^3$ N·mm $$ J=\Sigma A r^2=2A_A(12.90^2+60^2)+A_C(17.10^2)=1918015\ \text{mm}^4 $$ Torsional shear stress in a rivet: $\tau_t=\dfrac{Mr}{J}$ (perpendicular to the radius). #### Step 4 - resultant stresses **Rivet B** ($x=12.90$, $y=-60$): $\tau_x=\dfrac{My}{J}=64.38$ N/mm² (magnitude), $\tau_y=\tau_d+\dfrac{Mx}{J}=37.54$ N/mm² $$ \tau_B=\sqrt{64.38^2+37.54^2}=74.53\ \text{N/mm}^2 $$ **Rivet C** ($y=0$): $\tau_x=0$, $\tau_y=\tau_d-\dfrac{M\times17.10}{J}=5.35$ N/mm² $$ \tau_C=5.35\ \text{N/mm}^2 $$ **Answer: shear stress in rivet B (and A) $\approx74.5$ N/mm²; in rivet C $\approx5.3$ N/mm²**, both below the permissible 100 N/mm² of power-driven shop rivets. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What diameter is used for rivet area in this working stress solution? A. Nominal diameter d B. Hole diameter d0 = d + 1.5 mm C. d + 3 mm D. Shank diameter minus 1.5 mm Answer: B. The areas use the driven hole diameter, 17.5 mm and 21.5 mm. (Key point: Rivet areas) 2. Why is the centroid of the rivet group at 102.9 mm from the load line and not 105 mm? A. Rivet A and B are heavier B. Rivets are weighted by area, and C (larger) is at 120 mm C. The centroid is the average of the distances D. Load line is shifted Answer: B. Different diameters give different areas, so the centroid is area-weighted: (2 A_A x 90 + A_C x 120)/ΣA. (Key point: Centroid) 3. What is the direct shear stress in each rivet? A. 20000/240.5 = 83.2 N/mm^2 B. 20000 x 102.9 / 844.1 C. 20000/(3 x 363.1) D. 20000/844.1 = 23.69 N/mm^2, the same in every rivet Answer: D. Direct stress = P/ΣA, the same for all rivets. (Key point: Direct shear stress) 4. Why is the shear stress in rivet C only about 5.3 N/mm^2? A. C has larger area so it carries no load B. Torsional stress acts opposite to direct shear at C, which is on the far side of the centroid C. C lies on the load line D. Torsion does not act on C Answer: B. At C the torsional component acts against the direct shear: 23.69 - 18.34 = 5.35 N/mm^2. 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