--- title: "Mat foundation design procedure" subject: "Design of RCC Structure" chapter: 11 key: "semester_7/design_of_rcc_structure:mat-foundation-design-procedure" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/mat-foundation-design-procedure site: BCT Engineering --- # Mat foundation design procedure Design of RCC Structure · Chapter 11: Design of Footings - Asked in: 2081 Bhadra, 4 marks; 2075 Asoj, 5 marks; 2069 Chaitra, 6 marks (asked 3 times) - Video: [Design of Mat (Raft) Footing Manually | Excel Sheet IS 456:2000 | Multistorey Building |](https://www.youtube.com/watch?v=4MqXPFqQ1qU) — Parash Joshi - Civil Construction and Tutor - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/mat-foundation-design-procedure - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-11 ## Question Describe/explain in details all the design steps of R.C.C mat foundation design. ## Short answer First, size mat to keep resultant central and net pressure ≤ allowable bearing capacity. Determine depth from punching and one‑way shear. Analyze using rigid strip method or flexible (beam on elastic foundation) method. Compute bending moments, provide bottom steel under columns and top steel at mid‑spans, minimum 0.12% reinforcement. Check shear, development length, bearing; detail with 50 mm cover (75 mm without blinding). ## Answer A **mat (raft) foundation** is a large, continuous slab that supports the whole building (or several columns) and spreads the load over the full plan area. It is used when soil is weak, when isolated footings would cover more than about half the plan area, or to reduce differential settlement. #### Design steps 1. **Collect the data**: column loads and positions (dead + live, and moments), safe bearing capacity of the soil, grades of concrete and steel, depth of foundation. 2. **Find the resultant** of all column loads, $\sum P$, and its position $(\bar x, \bar y)$. Choose the plan size of the mat (with edge projections) so that its centroid coincides, or nearly coincides, with the resultant. Eccentricity $e = $ resultant - centroid should be small. 3. **Area**: $A = \dfrac{\sum P (1 + 0.1)}{q_{a}}$ (10% allowance for self-weight), and check that net upward pressure $$ q = \frac{\sum P}{A} \pm \frac{\sum P\, e_x}{Z_y} \pm \frac{\sum P\, e_y}{Z_x} \le q_a, \quad q_{min} \ge 0. $$ 4. **Choose the method of analysis**: - **Rigid (conventional) method**: if the column spacing is less than $1.75/\lambda$ (where $\lambda = \sqrt[4]{k_sB/4E_cI}$), the mat is taken as rigid. Contact pressure is linear. The mat is divided into strips between the column lines, each strip is analysed as a continuous beam under the pressure and the column loads, and the shear and bending moment diagrams are drawn. - **Flexible method** (beam on elastic foundation, or finite element/ plate on springs), when the mat is not rigid. 5. **Thickness**: determine the depth from **punching shear** around the heaviest columns (at $d/2$) and **one-way shear** at $d$ from the face of the column or wall (shear reinforcement is avoided when possible). Check also the bending requirement. 6. **Bending moments and reinforcement**: calculate positive and negative moments in each strip in both directions; design steel at top and bottom in each direction. Because the soil pressure acts upward and the columns act as supports, the bending is the reverse of a floor slab: **bottom steel** is needed under the columns and **top steel** at mid-span between columns. Provide minimum steel of 0.12% each way. 7. **Check** the development length, the bearing at the column base and the settlement. 8. **Detailing**: top and bottom mesh in both directions, extra bars at columns, cover 50 mm (75 mm if cast against the soil without blinding), dowels for the column bars, construction joints and waterproofing if below ground water. A mat can be a **plain slab**, a **slab with beams** (ribbed), or a **cellular/ box** type. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A mat foundation is typically preferred when A. The soil is very strong and loads are small B. Soil is weak or isolated footings would cover more than about half the plan area C. Only one column is present D. The water table is very deep Answer: B. A mat spreads load over the whole area, reducing pressure and differential settlement. (Key point: When to use a mat) 2. Why is the mat's centroid made to coincide with the resultant of column loads? A. To reduce eccentricity and keep soil pressure nearly uniform B. To increase the thickness C. To avoid reinforcement D. To raise the water table Answer: A. A small eccentricity keeps q_min >= 0 and pressure near uniform. (Key point: Plan size) 3. The mat is analysed by the rigid (conventional) method when A. Column spacing is less than 1.75/lambda B. Column spacing exceeds 1.75/lambda C. The soil is clay D. Columns are unequal Answer: A. Closely spaced columns make the mat rigid, giving linear contact pressure and strip analysis. (Key point: Rigid method) 4. The thickness of the mat is governed mainly by A. Punching shear around heavy columns (d/2) and one-way shear at d B. Temperature steel C. Soil colour D. Minimum steel 0.12% Answer: A. Depth is chosen from shear checks; top steel goes at columns and bottom steel at mid-span, with min 0.12% each way. (Key point: Thickness and steel) ## Related in Design of RCC Structure - [Beam-column joint with ductile details](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abeam-column-joint-with-ductile-details) — Design of RCC Structure, chapter 12, asked 2× - [Design steps of flanged beam sections](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-steps-of-flanged-beam-sections) — Design of RCC Structure, chapter 4, asked 2× - [Design steps of doubly reinforced section](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-steps-of-doubly-reinforced-section) — Design of RCC Structure, chapter 4 - [Design steps for long column, unbraced frame](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-steps-for-long-column-unbraced) — Design of RCC Structure, chapter 10 - [Steps of rectangular footing design](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Asteps-of-rectangular-footing-design) — Design of RCC Structure, chapter 11 - [Design of member for bending, shear, torsion](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-of-member-for-bending-shear) — Design of RCC Structure, chapter 5, asked 6× ## Related in other subjects - [Conventional design of mat foundation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-conventional-design) — Foundation Engineering, chapter 7, asked 3× - [Why design a mat foundation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awhy-design-mat) — Foundation Engineering, chapter 7 - [Steps of grounding mat design](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Agrounding-mat-design-steps) — Power Plant Design, chapter 4, asked 5× - [Compensated foundation and types of mat](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acompensated-foundation-mat-types) — Foundation Engineering, chapter 7, asked 7×