--- title: "Strut loads, 8 m cut in sand" subject: "Foundation Engineering" chapter: 4 key: "semester_5/foundation_engineering:strut-loads-8m-cut-sand" source: https://www.bctengineer.com/q/semester_5/foundation_engineering/strut-loads-8m-cut-sand site: BCT Engineering --- # Strut loads, 8 m cut in sand Foundation Engineering ยท Chapter 4: Arching in Soils and Braced Cuts - Asked in: 2073 Shrawan, 8 marks - Video: [Numerical On Strut ๐Ÿ”ฅ| Braced Cuts|Retaining Structure|Anchored Sheet Pile|Foundation](https://www.youtube.com/watch?v=mxEUMg8ja_0) โ€” DIPAK MANDAL - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/strut-loads-8m-cut-sand - Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-4 ## Question A 8 m deep cut in sand with a cut width of 5 m is braced at equal distance of 2 m from the surface at three locations. In the plan the struts are placed at a spacing of 4 m center to center. Using the empirical pressure diagram, calculate the design strut loads if the properties of sand is, angle of shearing resistance of $30^\circ$ and unit weight of $16\ \text{kN/m}^3$. (Also explain Terzaghi's trap door experiment with neat sketch.) ## Short answer Peck's sand diagram gives uniform pressure p = 0.65 Ka ฮณ H = 27.73 kN/mยฒ. Tributary area method yields reactions: A=83.2, B=55.5, C=83.2 kN/m. With 4 m spacing, design strut loads are A=333 kN, B=222 kN, C=333 kN. ## Answer #### Strut loads **Data:** $H = 8$ m, $\phi = 30^\circ$, $\gamma = 16$ kN/m$^3$, three struts at 2, 4 and 6 m below the ground, horizontal spacing $s = 4$ m. The width of the cut (5 m) does not affect the Peck envelope. **Apparent pressure (Peck, sand):** $$ K_a = \tan^2(45^\circ-15^\circ) = 0.3333,\qquad p = 0.65K_a\gamma H = 0.65\times0.3333\times16\times8 = 27.73\ \text{kN/m}^2 $$ The pressure is uniform over the full depth of 8 m (total 221.9 kN/m). ```text 0 | | 2m |--A-------| p = 27.73 4m |--B-------| 6m |--C-------| 8m |__________| ``` **Reactions (tributary-area method, each strut takes the load halfway to the next support; the bottom strut takes the load to the base):** | Strut | Tributary height | Reaction $R = p\times h$ (kN/m) | Strut load $P = R\times4$ (kN) | |---|---|---|---| | A (2 m) | 0 to 3 m = 3 m | 83.2 | 332.8 | | B (4 m) | 3 to 5 m = 2 m | 55.5 | 221.9 | | C (6 m) | 5 to 8 m = 3 m | 83.2 | 332.8 | Check: $\sum R = 221.9$ kN/m. **Answer: design strut loads A = 333 kN, B = 222 kN, C = 333 kN** (the same maximum, 333 kN, can be used for the top and bottom struts). #### Terzaghi's trap door experiment A box of dry sand has a base strip (trap door) that can be lowered. ```text sand surface ~~~~~~~~~~~~~~~~~~~~~~ | \ / | | \ yielding / | |____\__ wedge __/____| fixed | trap | fixed | door | v moves down ``` When the door moves down slightly the pressure on it falls sharply to about half of the overburden pressure, and the pressure on the neighbouring fixed base rises by the same total amount. Shear stresses along the nearly vertical planes carry part of the weight: this is **arching**. It explains why the earth pressure on braced cuts is not triangular but nearly uniform (Peck's envelope). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the apparent pressure for the braced cut in sand? A. 0.65 K_a gamma H, uniform over full depth B. K_a gamma H, triangular C. 0.65 K_a gamma H, triangular D. 0.3 gamma H trapezoidal Answer: A. Peck's sand envelope is uniform with p = 0.65 K_a gamma H = 27.73 kN/m^2. (Key point: Peck sand envelope) 2. How does the 5 m cut width affect the strut loads? A. Loads are multiplied by 5 B. It does not affect the Peck envelope C. Loads are divided by 5 D. It sets the strut spacing Answer: B. Peck's envelope depends on H, gamma and phi, not on cut width. (Key point: Role of cut width) 3. With struts at 2, 4 and 6 m in an 8 m cut, how much height does the bottom strut C carry? A. 2 m (from 5 to 7 m) B. 3 m (from 5 to 8 m) C. 4 m D. 1 m Answer: B. Each strut takes half the span to the next support; the bottom strut also takes the load down to the base, so 5 to 8 m = 3 m. (Key point: Tributary area) 4. What are the strut loads A, B, C (spacing 4 m)? A. 222, 333, 222 kN B. 333, 333, 333 kN C. 83, 55, 83 kN D. 333, 222, 333 kN Answer: D. R = 27.73 x 3 = 83.2 kN/m for A and C, 55.5 for B; times 4 m gives 333, 222, 333 kN. (Key point: Design strut loads) ## Related in Foundation Engineering - [Strut loads in braced cut](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astrut-loads-bracing-system) โ€” Foundation Engineering, chapter 4 - [Choosing pressure diagram for braced cut](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apressure-diagram-sand-clay-braced) โ€” Foundation Engineering, chapter 4 - [Define strut load and braced cut](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Adefine-strut-braced-cut) โ€” Foundation Engineering, chapter 4 - [Braced cut design versus retaining wall](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Abracing-vs-retaining-wall) โ€” Foundation Engineering, chapter 4, asked 2ร— - [Apparent pressure diagrams for braced cuts](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aapparent-pressure-diagrams) โ€” Foundation Engineering, chapter 4, asked 2ร— - [Soil pressure under rigid mat with column loads](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-rigid-soil-pressure-columns) โ€” Foundation Engineering, chapter 7 ## Related in other subjects - [Capacitor size, feeder with three equal loads](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Acapacitor-size-equal-loads-ohms) โ€” Transmission and Distribution System Design, chapter 7 - [Cut and fill volume, 20 m formation width](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-road-20m-width-cut-fill-1-1-1-2) โ€” Surveying I, chapter 9 - [Two-layer profile stress diagram, 6 m sand](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asand-clay-profile-stress-diagram-capillary) โ€” Soil Mechanics, chapter 6