--- title: "Compression capacity of double angle ISA 150x75x12" subject: "Design of Steel and Timber Structure" chapter: 6 key: "semester_6/design_of_steel_and_timber_structure:double-angle-compression-capacity" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/double-angle-compression-capacity site: BCT Engineering --- # Compression capacity of double angle ISA 150x75x12 Design of Steel and Timber Structure · Chapter 6: Compression Members - Asked in: 2079 Chaitra, 8 marks - 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/double-angle-compression-capacity - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-6 ## Question Determine design axial compressive load carrying capacity of a double angle IS 150×75×12 provided at opposite side of gusset plate, length of member is 3.5 m. ## Short answer Effective length 0.85×3500 = 2975 mm; minimum radius of gyration 29.8 mm gives slenderness 99.9, buckling class c, design stress 107.2 N/mm². Capacity = 5112 mm² × 107.2 = 548 kN. ## Answer **Data and assumptions:** 2 ISA 150×75×12 on opposite faces of a gusset plate (taken as 10 mm thick), long legs (150 mm) against the gusset, length $L=3.5$ m, steel E250 ($f_y=250$). The angles are connected at each end by at least two bolts (or welds), so (IS 800:2007 cl. 7.5.2) the effective length is taken as $KL=0.85L$ (between 0.7L and 1.0L depending on end restraint). Buckling class **c** for angles (Table 10). #### Section properties (from the leg-thickness rectangles) - Area of one angle $A_a=2556$ mm² (SP 6: about 2540 mm²), $c_x=17.1$ mm (from the back of the 150 mm leg) - One angle: $I_{xx}=591.9\times10^4$ mm⁴ (axis parallel to the 75 mm leg), $I_{yy}=102.0\times10^4$ mm⁴ (axis parallel to the 150 mm leg) - Pair: $A=2A_a=5112$ mm² - About the axis parallel to the gusset: $I_y=2[I_{yy}+A_a(t_g/2+c_x)^2]=453.5\times10^4$ mm⁴, $r_y=29.8$ mm - About the axis perpendicular to the gusset: $I_x=2I_{xx}=1183.8\times10^4$ mm⁴, $r_x=48.1$ mm - $r_{min}=29.8$ mm #### Slenderness and design stress $$ KL=0.85\times3500=2975\ \text{mm},\qquad \lambda=\frac{KL}{r_{min}}=\frac{2975}{29.8}=99.9\ (<180) $$ Using curve c ($\alpha=0.49$): $f_{cc}=\dfrac{\pi^2E}{\lambda^2}$, $\lambda_n=\sqrt{f_y/f_{cc}}$, $\phi=0.5[1+0.49(\lambda_n-0.2)+\lambda_n^2]$, $$ f_{cd}=\frac{f_y/\gamma_{m0}}{\phi+\sqrt{\phi^2-\lambda_n^2}}=107.2\ \text{N/mm}^2 $$ #### Capacity $$ P_d=A\,f_{cd}=5112\times107.2\times10^{-3}=548\ \text{kN} $$ Tack bolts (stitching) must be provided along the length so that the pair acts together: the slenderness of a single angle between them must not exceed 40 or $0.6\lambda$ of the whole strut, whichever is less (cl. 7.8), with at least two tack connections along the length. **Answer: design axial compressive capacity $\approx548$ kN.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which effective length is used for the double angle strut connected by at least two bolts at each end? A. KL = 1.0 L B. KL = 0.85 L C. KL = 2.0 L D. KL = 0.5 L Answer: B. IS 800 cl. 7.5.2 permits 0.85L (between 0.7L and 1.0L) for two or more bolts or welds at each end, so KL = 2975 mm. (Key point: Effective length of angle strut) 2. Which radius of gyration governs the slenderness of the pair? A. r_x = 48.1 mm B. r_y = 29.8 mm (about the axis parallel to the gusset) C. Average of both D. r_x of a single angle Answer: B. The smaller r_min = 29.8 mm governs, giving lambda = 2975/29.8 = 99.9. (Key point: Governing radius of gyration) 3. Once f_cd is obtained from buckling curve c, how is the capacity found? A. P_d = A f_cd = 5112 x 107.2 = 548 kN B. P_d = A f_y = 1278 kN C. P_d = A_a f_cd for one angle only D. P_d = f_cd / A Answer: A. The capacity uses the area of both angles: 5112 mm^2 x 107.2 N/mm^2 = 548 kN. (Key point: Compressive capacity) ## Related in Design of Steel and Timber Structure - [Double angle tension member, M18, same side](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atension-double-angle-300kn-m18) — Design of Steel and Timber Structure, chapter 5 - [Weld ISA 100x100x10 to 12 mm gusset](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Afillet-weld-angle-gusset-12mm) — Design of Steel and Timber Structure, chapter 4 - [Double angle tension member 300 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atension-double-angle-300kn) — Design of Steel and Timber Structure, chapter 5 - [Double angle tension member 400 kN, M20](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atension-double-angle-400kn-class-c) — Design of Steel and Timber Structure, chapter 5 - [Compression capacity of strut of two L75x75x8](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Astrut-two-l75x75x8) — Design of Steel and Timber Structure, chapter 6 - [Ultimate load of 2 ISA 100x100x8, M16 5.6](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atwo-angles-ultimate-load-m16) — Design of Steel and Timber Structure, chapter 5 ## Related in other subjects - [Timber-steel plate composite member: permissible load](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Atimber-steel-composite-permissible-load) — Strength of Materials, chapter 3 - [Double-stub on 75 Ω coax, load 0.4+j0.85](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adouble-stub-coax-normalized-load) — RF and Microwave Engineering, chapter 2 - [Double-stub on 75 Ω coax, load 109+j120 Ω](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adouble-stub-coax-109-j120) — RF and Microwave Engineering, chapter 2 - [Bearing capacity from plate load curve](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Abc-from-load-settlement-sand) — Foundation Engineering, chapter 6