Problem:

A rectangular start is 200mm wide and 150mm thick. It carries a load of 60kN at an eccentricity of 20mm in a plane bisecting the thickness. Find the maximum and minimum sensitivity of stress in the section.

Solution:

Given parameters:
- Width (b) = 200mm
- Thickness (h) = 150mm
- Load (P) = 60kN
- Eccentricity (e) = 20mm

Step 1: Calculate the moment of the load about the centroid of the section.

The moment (M) of the load about the centroid of the section can be calculated as:
M = P x e

Substituting the given values:
M = 60kN x 20mm
M = 1200Nm

Step 2: Calculate the position of the neutral axis.

The position of the neutral axis (NA) can be calculated as:
NA = (h/2) x (1 + (6M)/(bh^2P))

Substituting the given values:
NA = (150/2) x (1 + (6 x 1200Nm)/(200mm x (150mm)^2 x 60kN))
NA = 57.5mm

Step 3: Calculate the maximum and minimum stresses.

The maximum and minimum stresses can be calculated as:
- Maximum stress (σmax) = P/A + My/I
- Minimum stress (σmin) = P/A - My/I

where,
- A = bh
- I = bh^3/12
- y = distance from the neutral axis to the extreme fiber

Substituting the given values:
- A = 200mm x 150mm = 30000mm^2
- I = (200mm x (150mm)^3)/12 = 140625000mm^4
- y = (h/2) - NA = 150/2 - 57.5 = 22.5mm

σmax = 60kN/30000mm^2 + (1200Nm x 22.5mm)/(140625000mm^4/2 x 150mm)
σmax = 2MPa

σmin = 60kN/30000mm^2 - (1200Nm x 22.5mm)/(140625000mm^4/2 x 150mm)
σmin = -1.333MPa

Step 4: Interpretation of results.

The maximum stress is found to be 2MPa and the minimum stress is found to be -1.333MPa. The negative sign indicates that the stress is compressive. The maximum stress occurs at the top fiber of the section and the minimum stress occurs at the bottom fiber of the section.