--- title: "Rigid bar ABCD with brass and steel rods" subject: "Strength of Materials" chapter: 3 key: "semester_3/strength_of_materials:rigid-bar-abcd-brass-steel-15kn" source: https://www.bctengineer.com/q/semester_3/strength_of_materials/rigid-bar-abcd-brass-steel-15kn site: BCT Engineering --- # Rigid bar ABCD with brass and steel rods Strength of Materials · Chapter 3: Simple Stress and Strain - Asked in: 2079 Bhadra, 8 marks - Video: [PSAD Refresher 56: Analysis and Deformation Calculations on a Rigid Bar Assembly](https://www.youtube.com/watch?v=wwCNp7F4A2o) — Engr. Harf Miranda (Sir Harf Engineering Tutorial) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/rigid-bar-abcd-brass-steel-15kn - Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3 ## Question A rigid bar 'ABCD' is supported at 'A' and connected with a brass rod BE and a steel rod CF at 'B' and 'C' respectively as shown in the figure. A load of 15 kN is applied at 'D'. Find the magnitude of stress in the brass rod and for the steel rod. Take $A_b = 1000\ \text{mm}^2$, $A_s = 600\ \text{mm}^2$, $E_b = 100\ \text{kN/mm}^2$ and $E_s = 200\ \text{kN/mm}^2$. [Figure: horizontal rigid bar A-B-C-D with pin at A; A to B 2 m, B to C 2 m, C to D 1 m; brass rod BE of length 2 m hung from the ceiling at B; steel rod CF of length 3 m connecting C down to the ground at F; 15 kN downward load at D.] ## Short answer Equilibrium: Fb×2 + Fs×4 =75 kN·m. Compatibility: deflection of C is twice B, giving Fs =1.6Fb. Solving yields σbrass =8.93 N/mm² (tension) and σsteel =23.81 N/mm² (compression). ## Answer The load at D turns the bar clockwise about the pin A: B moves down and stretches the brass rod BE (tension, hung from the ceiling); C moves down and compresses the steel rod CF (standing on the ground). Let the forces be $F_b$ (tension) and $F_s$ (compression); the distances from A are B = 2 m, C = 4 m and D = 5 m. ```text ceiling ==========E================== | | brass (2 m) A-------2m--------B-------2m-------C---1m---D (pin) | | 15 kN | v | steel (3 m) ground ============================F========= ``` #### Equilibrium (moments about A) Both rods resist the load (brass pulls B up, steel pushes C up): $$ F_b(2) + F_s(4) = 15\times5 = 75\ \text{kN·m} $$ #### Compatibility The bar is rigid, so the deflection is proportional to the distance from A: $\delta_C = 2\delta_B$. $$ \frac{F_s(3000)}{600\times200} = 2\,\frac{F_b(2000)}{1000\times100} \;\Rightarrow\; 25\,F_s = 40\,F_b \;\Rightarrow\; F_s = 1.60\,F_b $$ (forces in kN with E in kN/mm²; both sides multiplied by 1000). #### Solution $$ \begin{aligned} 2F_b + 4(1.6F_b) &= 75 \Rightarrow F_b = 8.929\ \text{kN},\quad F_s = 14.286\ \text{kN}\\ \sigma_b &= \frac{8928.6}{1000} = 8.93\ \text{N/mm}^2\\ \sigma_s &= \frac{14285.7}{600} = 23.81\ \text{N/mm}^2 \end{aligned} $$ **Answer: $\sigma_{brass} = 8.93$ N/mm² (tension) and $\sigma_{steel} = 23.81$ N/mm² (compression).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What are the states of the rods under the load at D? A. Brass in tension, steel in compression B. Both in tension C. Both in compression D. Brass in compression, steel in tension Answer: A. B moves down stretching the hung brass rod; C moves down compressing the steel rod standing on the ground. (Key point: Rod nature) 2. Which moment equation about A is correct? A. 2F_b + 4F_s = 15 x 4 B. 2F_b + 4F_s = 15 x 5 C. F_b + F_s = 15 D. 4F_b + 2F_s = 15 x 5 Answer: B. B is 2 m, C is 4 m and D is 5 m from A, and both rods resist the load. (Key point: Equilibrium) 3. What compatibility relation links the rod deformations? A. delta_C = delta_B B. delta_C = delta_B / 2 C. delta_C = 2 delta_B D. delta_C = 5 delta_B / 2 Answer: C. A rigid bar rotating about A deflects in proportion to distance: C at 4 m, B at 2 m. (Key point: Compatibility) 4. What stress does the brass rod carry? A. 23.81 N/mm^2 B. 14.29 N/mm^2 C. 15 N/mm^2 D. 8.93 N/mm^2 Answer: D. F_b = 8.929 kN, stress = 8929/1000 = 8.93 N/mm^2 (steel 23.81). 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