--- title: "Bridge compression member, ISLC 400, toe to toe" subject: "Design of Steel and Timber Structure" chapter: 6 key: "semester_6/design_of_steel_and_timber_structure:bridge-compression-islc400" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/bridge-compression-islc400 site: BCT Engineering --- # Bridge compression member, ISLC 400, toe to toe Design of Steel and Timber Structure · Chapter 6: Compression Members - Asked in: 2070 Bhadra, 12 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/bridge-compression-islc400 - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-6 ## Question A bridge compression member is built using two channels ISLC 400 @ 45.8 kg/m placed toe to toe. The effective length of the member is 8.0 m. The width over the backs of two channels is 40 cm. The channels are properly connected by lacings. i) Calculate the safe load for the member. ii) Design the lacing systems using M16 property class 4.6 grade bolts. ## Short answer i) Factored safe load of the laced member is 2065 kN (service load ≈ 1377 kN). ii) Single lacing system: flat bars 60×12 mm, two M16 grade 4.6 bolts at each end. ## Answer **Approach.** Two channels toe to toe, laced; IS 800:2007 cl. 7.1.2 (compressive strength) and cl. 7.6 (laced columns). $f_y = 250$ N/mm² (E250), $f_u = 410$ N/mm², $\gamma_{m0} = 1.10$. Section properties of ISLC 400 @ 45.8 kg/m (IS 808; check against your steel table): $A = 58.3$ cm², $I_{xx} = 14000$ cm⁴, $I_{yy} = 462$ cm⁴, $C_{yy} = 2.37$ cm, $b = 100$ mm, $t_w = 8.0$ mm, $t_f = 14.0$ mm. #### (i) Safe load of the member The width over the backs is 400 mm, so the distance between the centroids of the channels is $h = 400 - 2C_{yy} = 400 - 47.4 = 352.6$ mm and the gap between the toes is $400 - 2\times100 = 200$ mm. $$ \begin{aligned} I_{zz} &= 2\times14000 = 28000\ \text{cm}^4,\quad r_{zz} = 15.50\ \text{cm} \\ I_{yy} &= 2[462 + 58.3\,(17.63)^2] = 37165\ \text{cm}^4,\quad r_{yy} = 17.85\ \text{cm} \\ \lambda_{zz} &= 8000/155.0 = 51.6,\quad \lambda_{yy} = 8000/178.5 = 44.8 \end{aligned} $$ Maximum slenderness $= 51.6$ (zz-axis). Laced column: $\lambda_{eff} = 1.05\times51.6 = 54.2$ (cl. 7.6.1.5). Buckling curve c ($\alpha = 0.49$, Table 10): $$ \begin{aligned} f_{cc} &= \frac{\pi^2E}{\lambda^2} = 672\ \text{N/mm}^2,\ \lambda_n = 0.610,\ \phi = 0.787,\ \chi = 0.779 \\ f_{cd} &= \chi f_y/\gamma_{m0} = 177.1\ \text{N/mm}^2 \\ P_d &= 2A f_{cd} = 2\times5830\times177.1/10^3 = 2065\ \text{kN} \end{aligned} $$ **Answer (i): safe (design) load $\approx 2065$ kN** (factored). Working load $= 2065/1.5 \approx 1377$ kN. #### (ii) Design of lacing (M16, grade 4.6 bolts, single lacing) Transverse shear $V_t = 2.5\%\,P = 0.025\times2065 = 51.6$ kN; per lacing plane $= 25.8$ kN (cl. 7.6.6.1). Bolt lines are at mid-flange, so $s = 200 + 100 = 300$ mm. Angle of lacing $\theta = 45^\circ$ (between 40° and 70°). $$ \begin{aligned} l &= s/\sin\theta = 424\ \text{mm} \\ F &= \frac{V_t/2}{\sin\theta} = 36.5\ \text{kN} \\ a_1 &= 2s\cot\theta = 600\ \text{mm} \end{aligned} $$ Check of the main member between lacing points: $a_1/r_{y} = 600/28.2 = 21.3$, below the smaller of 50 and $0.7\lambda_{max} = 36.1$. OK (cl. 7.6.5.1). Flat: width 60 mm ($\ge 3d = 48$ mm); thickness $\ge l/40 = 10.6$ mm and $\ge l\sqrt{12}/145 = 10.1$ mm, so use **ISF 60 × 12 mm**. $l/r = 122.5 \le 145$; $f_{cd} = 81.2$ N/mm², $P_{d,bar} = 720\times81.2/10^3 = 58.5$ kN $> 36.5$ kN. OK. Bolts M16, grade 4.6: $V_{dsb} = \frac{400}{\sqrt3}\times\frac{0.78\times\pi\times16^2/4}{1.25\times10^3} = 29.0$ kN; $V_{dpb} = 2.5k_bdtf_u/\gamma_{mb} = 87.5$ kN ($k_b = 0.556$, $t = 12$ mm). Bolt value $= 29.0$ kN, so the number of bolts $= 36.5/29.0 = 1.26$; provide **2 bolts M16 at each end of each bar**. Net section of the flat in tension: $A_n = (60 - 18)\times12 = 504$ mm², $T_{dn} = 0.9f_uA_n/\gamma_{m1} = 148.8$ kN $> 36.5$ kN. OK. End tie plates (cl. 7.6.8, 7.7.2): size $400\times360\times8$ mm (depth $\ge$ distance between centroids $= 353$ mm; thickness $\ge s/50 = 6$ mm). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Width over the backs is 400 mm and C_yy = 23.7 mm. What is the centroid-to-centroid distance h? A. 400 mm B. 376.3 mm C. 352.6 mm D. 200 mm Answer: C. h = 400 - 2 x 23.7 = 352.6 mm; the gap between toes is 400 - 2 x 100 = 200 mm. (Key point: Centroid distance) 2. lambda_zz = 51.6 and lambda_yy = 44.8. Which governs the safe load, and what slenderness is used? A. yy; 44.8 used directly B. zz; 1.05 x 51.6 = 54.2 C. yy; 1.1 x 44.8 D. zz; 0.7 x 51.6 Answer: B. The larger slenderness (zz) governs, and for a laced member it is multiplied by 1.05 to give 54.2. (Key point: Governing axis) 3. How is the design load obtained, and what value results? A. P_d = A f_y = 1460 kN B. P_d = 2 A f_cd = 2065 kN (factored); working load about 1377 kN C. P_d = 2 A f_cd = 1377 kN factored D. P_d = I f_cd = 2800 kN Answer: B. P_d = 2 x 5830 x 177.1 = 2065 kN factored; dividing by 1.5 gives about 1377 kN working load. (Key point: Safe load) 4. The lacing is designed for which transverse shear? A. 2.5% of the design load, shared by the lacing planes (51.6 kN total, 25.8 kN per plane) B. 10% of the design load C. The full load 2065 kN D. 2.5% of the working load per plane Answer: A. Cl. 7.6.6.1 takes 2.5% of axial load as transverse shear: 0.025 x 2065 = 51.6 kN, 25.8 kN per plane. (Key point: Lacing design basis) ## Related in Design of Steel and Timber Structure - [Built-up column, two channels toe-to-toe, 1500 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-1500kn-10m-toe-to-toe) — Design of Steel and Timber Structure, chapter 6 - [Bridge compression member, 1200 kN, tie bar lacing](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abridge-compression-1200kn-tie-bar) — Design of Steel and Timber Structure, chapter 6 - [Column with two channels toe to toe, 1200 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-toe-to-toe-lacing-1200kn-6m) — Design of Steel and Timber Structure, chapter 6 - [Built-up column with battens, 6 m, 1200 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-battens-1200kn-6m) — Design of Steel and Timber Structure, chapter 6 - [Tension member with lug angle, 400 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atension-lug-angle-400kn) — Design of Steel and Timber Structure, chapter 5, asked 2× - [Built-up beam, unsupported 4 m, 40 kN/m + 100 kN](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuiltup-beam-unsupported-4m-40knm) — Design of Steel and Timber Structure, chapter 7 ## Related in other subjects - [Two blocks connected over a pulley](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_mechanics%3Ablocks-pulley-friction-acceleration) — Engineering Mechanics, chapter 2 - [Image by two lenses 30 cm and 40 cm](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Atwo-lenses-thirty-forty-image) — Engineering Physics, chapter 5, asked 3× - [Suspension 400 m: max/min tension, cable length](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Asuspension-400m-dip30-3x300kn) — Theory of Structures I, chapter 7, asked 3× - [Nichrome strip width for 40 kW 3-phase oven](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Anichrome-strip-40kw-oven-width) — Utilization of Electrical Energy, chapter 5, asked 2×