❓ What is Shear?

Shear is a force that acts parallel to a cross-section of structural memeber, causing one part of a structural member to slide or move relative to another part.

In reinforced concrete beams, shear failure usually occurs near the supports, where the beam is carrying loads and transferring them to columns or walls. If the shear force is too large, diagonal cracks may form in the concrete.

Shear Failure

❓ What is Shear Resistance?

Shear resistance is the ability of a structural member to resist shear force without failing.

In reinforced concrete design, shear resistance is usually provided by:

  1. Concrete, before it crack, details mentioned in this articles
  2. Shear reinforcement, such as stirrups or shear links, which helps carry shear after diagonal cracks form, details is discussed below.

Common symbol in eurocode:

VRd
θ Compression Struct Tension Ties Shear, V inner lever arm, z Truss Model for Shear Analysis

🧩 Dependance of Shear Resistance from Reinforcement

From Eurocode 2, VRd,s mainly depends on: Cl. 6.2.2, BSEN 1992-1-1:2004

zcotθ s Asw Top Section Section View
  • Inclined angle of compression strut, θ
  • Corss-sectional area of shear reinforcement, As
  • Spacing of the link, s
  • Design yield strength of shear reinforcement, fywd
  • Internal lever arm, z (mainly affected by effective depth, d)
  • Section width, bw

🔍 Details of Formula of VRd,s and VRd,max

The Shear Resistance provided by vertical shear links can be calculated in below formula Eq. 6.8 & 6.9, BSEN 1992-1-1:2004, details about how it come from can refer to here

Shear Resistence from vertical reinforcement
Eq. 6.8, BSEN 1992-1-1:2004
where
Asw = corss-sectional area of shear reinforcement
s = spacing of the links
z = internal lever arm
fywd = design yield strength of shear reinforcement
θ= inclined degree of compression struct
Maximum Shear Resistance
Eq. 6.9, BSEN 1992-1-1:2004
where
αcw= coeff. for stress in compression chord, take 1 for non-prestressing case
bw =
v1 = v = , strength reduction factor for concrete cracked in shear
θ= inclined degree of compression strut

Case 1: Given a section with Shear links Asw/s, find the Shear capacity

Width, bw Depth, d Given shear links Asw/s Find Shear Capacity, V Rd Section
1

Calculate inclined angle θ by equaling VRd,s = VRd,max

By rearranging VRd,s = VRd,max,

θ = 0.5sin-1(Aswfywd/(bwsvfcd))

2

Check againest θ within EC2 limit, eq. 6.7N

22.5° ≤ θ ≤ 45° as the limit is 1 ≤ cotθ ≤ 2.5

3

Calculate Shear Capacity from shear links VRd,s

VRd,s = (As/s)zfywdcotθ

4

Check Shear Capacity from shear links exceed maximum shear resistence by concrete strut

VRd = min(VRd,s, VRd,max)

Case 2: Given a Shear Force VEd, find the required shear reinforcement area

Width, bw Depth, d Find shear links Asw/s Given Shear Force, V Ed Section
1

Calculate Concrete Shaer Resistance, VRd,c

VRd,c = [CRd,ck(100ρlfck)0.33 + k1σcp]bwd

2

Check against VEd and VRd,c, if shear link need

If VEd < VRd,c, if slab, no need shaer link; if beam, only minimum shear link need

If VEd > VRd,c, shear link is required, and see step 3

3

Calculate inclined angle θ by equaling VEd = VRd,max

θ = 0.5sin-1(2VEd/(αcwvfcdbwz))

4

Check againest θ within EC2 limit, eq. 6.7N

22.5° ≤ θ ≤ 45° as the limit is 1 ≤ cotθ ≤ 2.5

5

Calculate required shear links Asw/s, by equaling VEd = VRd,s

Asw/s = VEd/(zfywdcotθ)

📝Summary & Key Takeaways

  1. Shear is a force that acts parallel to the cross-section of a structural member. Shear failure is commonly associated with the formation of diagonal tension cracks.
  2. Shear resistance is provided by concrete before cracking and by shear reinforcement after cracking.
  3. Common shear calculation procedures are demonstrated in this article, including determining the shear capacity of a given section with shear links and calculating the required shear reinforcement area for a given shear force.
#rc design #shear design #glossary #structural
CivilSimple Team

CivilSimple Team

The CivilSimple Team writes practical engineering guides for the profession and the curious. All articles are reviewed for technical accuracy before publication.