Question 3.2: The inner diameter of a boiler with cylindrical shape is 2.5...

Had the boiler been made up of a single piece of metal without any longitudinal or circumferential joints/connections, the allowable stress could have been considered for design. However, in the present problem, there are joints and as expected they have efficiency <100%.
As the boiler is cylindrical, we should first select the significant stress, that is, the circumferential stress for calculation and try to find out the ‘thickness’. We can write

\sigma_1=\frac{p r}{\eta t}

where t is the thickness of the plate and η is the efficiency of circumferential joint. Substituting the given values, we get

100=\frac{2.0 \times(2.5 \times 1000) / 2}{t \times 0.7}

or         t = 35.71 mm

If we had a single piece of metal, we could have stopped here saying that the thickness is 35.71 mm. However in this case, we have circumferential joints as well as longitudinal joints with separate efficiencies. So, we will also have to find ‘t’ from the consideration of longitudinal stress and select the higher value of ‘t’. For longitudinal joints,

\sigma_2=\frac{p r}{2 \eta t}

or          100=\frac{2.0 \times(2.5 \times 1000) / 2}{2 \times 0.5 \times t}

or          t = 25 mm

We have two values of ‘t’; the higher one provides safety. So, the desired thickness is 35.71 mm.