DT EC 01: Shear

Description

Geometry	Cross-section:	70x221mm
Geometry	Material:	C24
Load	ULS FC:	7.16kN
Standard		EN 1995-1-1 [- -]
Design parameters	k_mod:	0.8

Independent reference results

Open handcalculations

According to EN 1995-1-1 §6.1.7 (1)P the shear check implies:

$\tau_d \leq f_v_._d$

with

$\tau_d$ the design shear stress
$f_v_._d$ the design shear strength (= a material property)

From any course on mechanics, you can find that the maximal shear stress in a rectangular section equals:

$\tau_d=\frac{3 \cdot V_E_d}{2 \cdot A}$

Combining both equations gives:

$\frac{3 \cdot V_{Ed}}{2 \cdot A} \leq f_v_._d$

$V_{Ed} \leq \frac{2 f_v_._d \cdot A}{3}$

The area $A$ of a rectangular section equals $b \cdot h$ :

$V_{Ed} \leq \frac{2}{3} b \cdot h \cdot f_v_._d$

Yet EN 1995-1-1: 2004/A1:2008 §6.1.7 (2) states that the effective width $b_{eff} = b \cdot k_{cr}$ ; should be used instead of the width $b$ to take the influence of cracks into account. $k_{cr} = 0.67$ for solid and glued laminated timber, $k_{cr}= 1.0$ for all other wood based products.

$V_{Ed} \leq \frac{2}{3} \cdot b_{eff} \cdot h \cdot f_{v.d}$

$\begin{align*} UC&= \frac{V_{Ed}}{\frac{2}{3} \cdot k_{cr} \cdot b \cdot h \cdot f_{v.d}}\\ &= \frac{V_{Ed}}{\frac{2}{3} \cdot \frac{2}{3} \cdot b \cdot h \cdot f_{v.d}}\\ &= \frac{7.2 \text{kN}}{\frac{2}{3} \cdot \frac{2}{3} \cdot 70 \text{mm} \cdot 221 \text{mm} \cdot \frac{4 \text{N/mm²}}{1.3}}} \\ L_{eff}&= \frac{L}{C_1} +2 \cdot h \text{ general case}\\ \end{align*}$

$\begin{align*} UC &= \frac{V_{Ed}}{\frac{2}{3} \cdot k_{cr} \cdot b \cdot h \cdot f_{v.d}}\\ &= \frac{V_{Ed}}{\frac{2}{3} \cdot \frac{2}{3} \cdot b\cdot h \cdot f_{v.d}}= \frac{V_{Ed}}{\frac{2}{3} \cdot \frac{2}{3} \cdot b\cdot h \cdot \frac{k_{mod } \cdot f_{v.k}}{\gamma_m} }\\ &= \frac{7.16kN}{\frac{2}{3} \cdot \frac{2}{3} \cdot 70 \text{mm} \cdot 221 \text{mm} \cdot \frac{0.8 \cdot 4 \text{N/mm²}}{1.3}}\\ &=42.3 \% \end{align*}$

Diamonds results and comparison

Strength verification of the beam according to EN 1995-1-1. At the end of the bar, the shear is decisive. In the middle of the beam it’s bending.

Intermediate results in Diamonds for lateral torsional buckling

Results	Independent reference	Diamonds	Difference
Unity check	42.3%	42.1%	-0.47%

References

- EN 1995-1-1: 2005 + AC: 2006

Tested in Diamonds 2025.

Article Attachments

.bsf

DT EC 01 72 KB

Was this article helpful?

Yes No

Need Support?

Can't find the answer you're looking for? Don't worry we're here to help!

CONTACT SUPPORT