1495x

Hedi Boukraa, B.Sc.

2024-02-28

VE 1024 | Shear at Interface Between Concrete Cast According to DIN EN 1992-1-1

Description

In this example, the shear at the interface between concrete cast at different times and the corresponding reinforcement are determined according to DIN EN 1992-1-1. The obtained results with RFEM 6 will be compared to the hand calculation below.

The Model consists of 2.812 m T-beam, fixed in one end. The shear section is shown in the figure below.

Verification Example 1024 | Shear at Interface Between Concrete Cast

Material	Concrete C25/30	Modulus of Elasticity	E	31000	N/mm²
	Concrete C25/30	Design value of concrete compressive strength	f_cd	14.167	N/mm²
	Reinforcing steel B500S(A)	Characteristic yield strength	f_yk	500.000	N/mm²
	Reinforcing steel B500S(A)	Design yield strength	f_yd	434.783	N/mm²
Geometry	T-beam	Height	h	1350	mm
		Effective depth	d	1280	mm
		Flange height	h_f	290	mm
		Flange width	b_eff	2500	mm
		Web width	b_w	400	mm
Load	Permanant loads	Nodal load		800.0	kN

The T-beam is modelled in RFEM 6 using the member type Rib.

Analytical Solution

The inner forces at the end of the cantilever are summarized in the following table:

Inner Forces
Type	Symbole	Unit	Result
Design shear force	V_Ed	[kN]	800
Design bending moment	M_Ed	[kNm]	2250

The area of tensile reinforcement is calculated using dimension tables:

µ_{Eds} = \frac{M_{Eds}}{b_{eff} \cdot d^{2} \cdot f_{cd}} = \frac{2250 \cdot 10^{- 3}}{2.5 \cdot 1 . 28^{2} \cdot 14.17} = 0.03876

where

ω = 0.03971

ξ = 0.9766

Related Moment µ

A_{s 1} = \frac{1}{σ_{sd}} \cdot (ω \cdot b \cdot d \cdot f_{cd} + N_{Ed}) = \frac{1}{456.52} \cdot (0.03971 \cdot 2.5 \cdot 1.28 \cdot 14.17) = 39.44 {cm}^{2}

Tensile Reinforcement

Next, the design shear stress v_Edi and the design shear resistance v_Rd,c are determined:

v_{Edi} = β \cdot \frac{V_{Ed}}{z \cdot b_{i}} = 1.0 \cdot \frac{800 \cdot 10^{3}}{1152 \cdot 400} = 1.736 N / {mm}^{2}

where

β = 1.0

z = 0.9 \cdot d = 0.9 \cdot 1280 = 1152 mm

Design Value of Shear Stress acc. to DIN EN 1992-1-1, 6.2.5 (1)

v_{Rd, c} = C_{Rd, c} \cdot k \cdot {(100 \cdot ρ_{l} \cdot f_{ck})}^{1 / 3} + k \cdot σ_{cp} = 0.10 \cdot 1.3953 \cdot {(100 \cdot 0.00703 \cdot 25)}^{1 / 3} + 0.10 \cdot 0 = 0.37323 N / {mm}^{2}

where

C_{Rd, c} = 0.15 / γ_{c} = 0.15 / 1.5 = 0.10

k = 1 + \sqrt{\frac{200}{1280}} = 1.3953 \leq 2.0

ρ_{1} = \frac{A_{sl}}{40 \cdot 128} = 0.007703 \leq 0.02

Design Value of Shear Resistance According to DIN EN 1992-1-1, 6.2.2 (1)

v_Edi is superior to v_Rd,c. Therefore, shear reinforcement is required:

v_{Rdi} = c \cdot f_{ctd} \cdot μ \cdot σ_{n} + ρ \cdot f_{yd} \cdot (1.2 \cdot μ \cdot \sin (α) + \cos (α)) = 0.5 \cdot 1.02 + 0.9 \cdot 0 + \frac{0}{0.4} \cdot 435 \cdot (1.2 \cdot 0.9 \cdot 1 + 0) = 0.510 N / {mm}^{2}

Design Shear Resistance at Interface Without Shear Reinforcement acc. to DIN EN 1992-1-1, (NDP) 6.2.5 (1)

v_{Rd, \max} = 0.5 \cdot ν \cdot f_{cd} = 0.5 \cdot 0.70 \cdot 14.167 = 4.958 N / {mm}^{2}

where

ν = 0.70 for the indented interface

Mximum Value of Design Shear Resistance at Interface acc. to DIN EN 1992-1-1, 6.2.5 (1)

v_{Rdi} = c \cdot f_{ctd} \cdot μ \cdot σ_{n} + ρ \cdot f_{yd} \cdot (1.2 \cdot μ \cdot \sin (α) + \cos (α)) = 0.5 \cdot 1.02 + 0.9 \cdot 0 + \frac{a_{s}}{0.4} \cdot 435 \cdot (1.2 \cdot 0.9 \cdot 1 + 0)

\to 0.51 + \frac{a_{s}}{0.4} \cdot 469.56 = 1.736 N / {mm}^{2}

\to a_{s} = 10.44 {cm}^{2} / m

Design Shear Resistance at Interface acc. to DIN EN 1992-1-1, (NDP) 6.2.5 (1)

RFEM Settings

In the Rib setting, shear joint between flange and web is activated.
The roughness classification is set to Indented

Results

Designation	Variable	Unit	RFEM result	Analytical solution	Ratio
Roughness factor c	c	[-]	0.5	0.5	1.0
Roughness factor	μ	[-]	0.9	0.9	1.0
Strength reduction factor for concrete cracked in shear for joints	ν	[-]	0.7	0.7	1.0
Inner lever arm	z	[m]	1.179	1.152	1.02
Ratio of longitudinal force in new concrete area and total longitudinal force	β	[-]	1.0	1.0	1.0
Angle	α	[°]	90	90	1.0
Design value of shear stress in interface	v_Ed,i	[N/mm²]	1.695	1.736	0.98
Maximum design shear resistance at the interface	v_Rd,i,max	[N/mm²]	4.958	4.958	1.0
Design shear resistance at the interface without shear reinforcement	v_Rd,i	[N/mm²]	0.510	0.510	1.0
Required shear reinforcement at the interface	a_sw,i,req	[cm²/m]	10.10	10.44	0.97

Results

The RFEM 6 results obtained are highly accurate. The observed slight deviations primarily stem from the calculation of the inner lever arm, z. In the analytical solution, z is simply considered as 90% of the effective depth, whereas RFEM calculates it precisely.

T-Beam - Shear at Interface Between Concrete Cast

532x

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Verification Example 1024 | Shear at Interface Between Concrete Cast of T-Beam

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