Are you embarking on a construction project and aiming for structural excellence? Understanding the intricacies of shear checks for pad footings is paramount to ensure the stability and safety of your structure. In compliance with Eurocode 7 (EC 7), a comprehensive analysis of shear forces becomes imperative. This guide is your key to navigating the complexities of checking shear for pad footings according to EC 7. From the fundamentals of shear force to the specific requirements outlined in the Eurocode, we’ll unravel the critical steps to guaranteeing the structural integrity of your pad footings. Let’s look into the world of shear checks and empower your construction endeavors with knowledge and compliance.

## How to Check Shear for Pad Footings according to EC 7

Shear checks for pad footing design according to EC 7 is carried out at the face of the column and at the basic control perimeter U_{1}. If shear reinforcement is required a further perimeter U_{out,ef} should be found where shear reinforcement is no longer required. In footings, the load within the control perimeter adds to the resistance of the structural system, and may be subtracted when determining the design punching shear stress.

The shear check can be carried out in the following steps:

**Step 1: **Determine the value of design shear stress at the face of the column (V_{Ed,max})

Where:

V_{Ed} is the applied shear force

ΔV_{Ed} is the net upward force within the control perimeter considered i.e. upward pressure from soil minus self-weight of base.

U_{o} = the column perimeter = c_{2} + 3d ≤ c_{2} + 2c_{1} (mm) for edge column and 3d ≤ c_{1} + c_{2} (mm) for corner column.

c_{1}, c_{2} are the column dimensions as shown in Figure 3.

Where:

d_{y} and d_{z} are effective depths of the reinforcement in orthogonal directions (see Figure 4)

β = 1.0 when the applied moment is zero. When there is moment (for eccentric loading), β should be determined with the expression below:

Where:

u_{1} is the length of the basic control perimeter

k is a coefficient dependent on the ratio between the column dimensions c1 and c2: its value is a function of the proportions of the unbalanced moment transmitted by uneven shear and by bending and torsion.

*Table 1:** Values of k for rectangular loaded areas*

c |
≤ 0.5 | 1.0 | 2.0 | ≥3.0 |

k | 0.45 | 0.60 | 0.70 | 0.80 |

W_{1} corresponds to a distribution of shear and is a function of the basic control perimeter u_{1}:

Where:

dl is a length increment of the perimeter

e is the distance of dl from the axis about which the moment M_{Ed} acts

**For rectangular columns,**

Where:

c_{1} is the column dimension parallel to the eccentricity of the load

c_{2} is the column dimension perpendicular to the eccentricity of the load

**For internal circular columns,**

Where:

D is the diameter of the circular column

e is the eccentricity of the applied load, e = M_{Ed} / V_{Ed}

Other cases where β varies are:

- An internal rectangular column where the loading is eccentric to both axes.
- For edge column connections, where the eccentricity perpendicular to the slab edge (resulting from a moment about an axis parallel to the slab edge)

**Step 2:** Determine the value of maximum design shear resistance, V_{Rd,max}. This value is usually picked from Table 2 below but can be calculated using the expression below:

Where:

a is the distance from the periphery of the column to the control perimeter considered.

f_{ck} is in MPa

Otherwise, the values of V_{Rd,max} can be picked from Table 2

**Table 2:** Values of V_{Rd,max}

f_{ck} |
V_{Rd,max} |

20 | 3.68 |

25 | 4.50 |

28 | 4.97 |

30 | 5.28 |

32 | 5.58 |

35 | 6.02 |

40 | 6.72 |

45 | 7.38 |

50 | 8.00 |

Where ρ_{1} exceeds 0.40%, the following factors may be used:

f_{ck} |
25 | 28 | 32 | 35 | 40 | 45 | 50 |

Factor, ρ_{1} |
0.94 | 0.98 | 1.02 | 1.05 | 1.10 | 1.14 | 1.19 |

**Step 3:** If V_{Ed,max} > V_{Rd,max}, redesign the foundation

**Step 4:** V_{Ed,max} < V_{Rd,max}, determine the value of design shear stress (V_{Ed}):

Where:

u_{1} = length of control parameter for concrete footing – see Figures 3 or 4

For eccentrically loaded footings, the control parameter will have to be found through iteration; it will usually be between d and 2d.

**Step 5:** Determine the concrete punching shear capacity, V_{Rd} (without shear reinforcement) from:

The values of V_{Rd,c} can be picked from Table 3 but can be calculated using the expression below for depths greater than 1000.

**Step 6:** If V_{Ed} > V_{Rd} at critical perimeter, either increase the main steel or provide punching shear reinforcement required (though not recommended for foundations)

**Step 7:** If V_{Ed} < V_{Rd}, no shear reinforcement is required.

**Step 8:** Shear checks complete

## CONCLUSION

As we conclude our exploration into checking shear for pad footings according to EC 7, it’s evident that adherence to Eurocode standards is the cornerstone of a robust and secure foundation. By mastering the art of shear force analysis, you not only ensure compliance with industry regulations but also elevate the resilience of your structures. Remember, the strength of a building lies in the meticulousness of its foundation, and with the insights gained here, you’re well-equipped to navigate the challenges and guarantee the structural soundness of your pad footings. Harness the power of knowledge, embrace EC 7 guidelines, and embark on your construction journey with confidence and competence.