Problem 3.7. Glued connection

Shear stress at the glued surface, τ [N/mm²]=

Step 1.  Draw the shear force diagram along the length of the beam. Determine the maximum shear force.

Check shear force diagramHide shear force diagram

Step 2. Calculate the shear stresses along the height of the cross section. Give the shear stress at the clued surface.

Check shear stressesHide shear stresses

Shear stresses are determined by the Zhuravskii formula, results are given in the Figure.

Eq.(3-34)

The relevant shear stress arises below the top flange:

$\mathit{\tau }=\frac{VS}{Ib}=\frac{38.33\times {10}^3\times 2480247}{9.825\times {10}^8\times 50}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{94}\frac{\mathbf{N}}{\mathbf{m}{\mathbf{m}}^{\mathbf{2}}}$

where the center of gravity and the moment of inertia of the cross section is calculated in the previous problem, and the moment of area is:

$S=b_1{t}_1\left(s–\frac{t_1}{2}\right)=2.48\times {10}^6{\mathrm{mm}}^3$

Step 3. Perform shear check

CheckHide

The glued surface is subjected to shear. The shear force diagram can be determined from the geometry and load given in the previous problem. The moment diagram given before also helps the calculation.

The maximum shear force arises at the left side of the middle support:

$V^{{}_{\max }}=A–pl=\frac{M^{\max }}{L}+\frac{pl}{2}–pl=\frac{M^{\max }}{L}–\frac{pl}{2}=\frac{–50}{6}–\frac{10\times 6}{2}=38.33 \mathrm{kN}$

Shear stresses are determined by the Zhuravskii formula, results are given in the Figure.

Eq.(3-34)

The relevant shear stress arises below the top flange:

$\mathit{\tau }=\frac{VS}{Ib}=\frac{38.33\times {10}^3\times 2480247}{9.825\times {10}^8\times 50}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{94}\frac{\mathbf{N}}{\mathbf{m}{\mathbf{m}}^{\mathbf{2}}}$

where the center of gravity and the moment of inertia of the cross section is calculated in the previous problem, and the moment of area is:

$S=b_1{t}_1\left(s–\frac{t_1}{2}\right)=2.48\times {10}^6{\mathrm{mm}}^3$

The shear check is performed at the glued surface:

$\tau =1.94\frac{\mathrm{N}}{{\mathrm{mm}}^2}>f=1\frac{\mathrm{N}}{{\mathrm{mm}}^2}$

The shear stress exceeds the strength of the glue, thus the connection is not adequate.