Solution ## Data- **Vertical load on cap**: P = \,text{kN \) - **Moment on pile**: \( =180\,\{kN}\ot\textm} \) - **Number of piles**: \( n = \- **Pile arrangement**: Square - **Pile spacing (center to center)**: \( s = 1.2\,\text{m} \) **able capacity pile**: \( Q_\text{all} =500\,\text{kN}) - ** skin friction per**: \( N_\text{neg} 55\,\text{kN} \## Step 1: Pile Layout The piles are at corners of a square. For moment calculations, define axes through the centroid. - **Centroid to pile distance( a \))**: Each pile is at corner so distance from centroid to pile is \[ a = \{s}{2} \] For square, the moment can act about any axis; let's assume it acts about the centroid in one direction. ## Step2: Load Distribution Without Moment If only vertical load(P\)), each pile carries: \[ Ptext{vertical,each} = \frac{P}{n} = \frac{160}{4} = 400\,\text{kN} \] ## Step 3: Effect of Moment moment causes additional axial load on the piles, depending on position. For a square: - Let’s assume the moment acts about the centroid is parallel to one side. For a square with spacing \( s \), the lever arm from to pile in the moment direction is \( a = s2 \). The **axial due to moment** on each pile: \[ Q_M = \frac{M \cdot y}{\sum y^2} \] where \( y \) is the coordinate of each pile from the centroid (either \( +a \) or \( -a \)), and the denominator is the sum for all piles. For this arrangement: - Two piles have \( y = + \), two have \( y = -a \) - \sum y^ =2(a^2 + a^2) = 4a^2\) So, the **additional load per pile** is: \[ Q_M = \frac{M \cdot a}{4a^2} = \fracM}{4a} \] - Two piles get \( +Q_M \) (compression) - Two piles get \( -Q_M \) (tension, reduces axial load) ### Calculate \( a \): \[ a \frac{s}{2} = \frac{1.2}{2} = .6\,\text{m} \] \[ _M = \frac{180}{4 \times .6} = \frac{}{.4} 75\,\text{kN} \] ## Step 4: Maximum and Minimum Pile Loads \\text{Maximum pile load} = P_\text{vertical,each} + Q_M = 400 + 75 =475\,\text{kN} \] [ \text{Minimum pile load} = 400 - 75 = 325\,\text{kN} \] ## Step 5: Include Negative Skin Friction Negative friction **ward** (adds to structural load). \[ \text{Maximum pile load (with negative skin friction)} = 475 + 55 = 530\,\text{kN} \] \[ \text{Minimum pile load (with negative skin friction)} = 325 55 = 380\,\{kN} \] ## Step 6: Check Against Allowable Capacity \[ \text{able capacity per pile} = \,\text{kN} \] \[ \text{Maximum pile (with negative friction = 530\,\text{kN} 500\,\text{kN} \] **Therefore, the maximum pile load exceeds the allowable capacity.** --- ## **Summary Table** | Pile Vertical (N) | Moment Load (kN) | Negative Friction (kN) | Total Load (kN) | |-----------|--------------------|----------------|----------------------------------------------| Max loaded| 400 |75 |55 | **530** | | Min loaded| 400 | -75 | 55 | | --- # **** - **Maximum pile load:** **530 kN** - **Allowable pile capacity:** **500 kN** - **Result:** The foundation **does not** allowable axial capacity requirement. pile must be revised (increase pile capacity, add more piles, or reduce loads).