Problem 4.9. Eccentrically compressed masonry wall

Plastic resistance, N_R,p [kN]=

Elastic resistance, N_R,e [kN]=

Ratio of plastic and elastic resistances, N_R,p/N_R,e =

Follow steps of Example 4.2.

Step 1. Perform plastic analysis. Draw normal stress diagram. Calculate the length of the compressed part of the wall.

Check compressed lengthHide compressed length

See Figure 4.16.

$h_{\mathrm{c}}=2\left(\frac{h}{2}–e\right)=2\left(\frac{4.0}{2}–0.76\right)=2.48 \mathrm{m}$

Step 2. Determine plastic load-bearing capacity of the cross section.

Check plastic resistanceHide plastic resistance

Eq.(4-27)

${\mathit{N}}_{\mathbf{R}\mathbf{,}\mathbf{p}}= h_{\mathrm{c}}b{f}_{\mathrm{c}}=2480\times 300\times 1.74=1294.6\times {10}^3 \mathrm{N}\mathbf{=}\mathbf{1294}\mathbf{.}\mathbf{6}\mathbf{ }\mathbf{kN}$

Step 3. Perform elastic analysis. Draw normal stress diagram. Calculate the length of the compressed wall part.

Check compressed lengthHide compressed length

Step 4. Determine elastic load-bearing capacity of the cross section.

Check elastic resistanceHide elastic resistance

Step 5. Give the ratio of plastic and elastic resistance.

Check ratioHide ratio

Follow steps of Example 4.2.

First plastic analysis is performed. Normal stress diagram is given in the Figure below. 

See Figure 4.16.

The length of the compressed part of the wall is$h_{\mathrm{c}}=2\left(\frac{h}{2}–e\right)=2\left(\frac{4.0}{2}–0.76\right)=2.48 \mathrm{m}$

The plastic load-bearing capacity of the cross section can be determined from the stress diagram:

Eq.(4-27)

${\mathit{N}}_{\mathbf{R}\mathbf{,}\mathbf{p}}= h_{\mathrm{c}}b{f}_{\mathrm{c}}=2480\times 300\times 1.74=1294.6\times {10}^3 \mathrm{N}\mathbf{=}\mathbf{1294}\mathbf{.}\mathbf{6}\mathbf{ }\mathbf{kN}$

Now elastic analysis is performed. The normal stress diagram is shown in the Figure.

$h_{\mathrm{c}}=3\left(\frac{h}{2}–e\right)=3\left(\frac{4.0}{2}–0.76\right)=3.72 \mathrm{m}$

At limit stage normal stress in the outermost points of the cross section reaches the value of normal strength, see stress diagram above. Elastic resistance can be calculated from the stress diagram:

${\mathit{N}}_{\mathbf{R}\mathbf{,}\mathbf{e}}= \frac{1}{2}{h}_{\mathrm{c}}b{f}_{\mathrm{c}}=\frac{1}{2}3720\times 300\times 1.74=970.9\times {10}^3 \mathrm{N}\mathbf{=}\mathbf{970}\mathbf{.}\mathbf{9}\mathbf{ }\mathbf{kN}$

The ratio of plastic and elastic resistance is

$\frac{{\mathit{N}}_{\mathbf{R}\mathbf{,}\mathbf{p}}}{{\mathit{N}}_{\mathbf{R}\mathbf{,}\mathbf{e}}}= \frac{1294.6}{970.9}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{33}$