Staircase Regulations

I'm considering a loft extension and it requires a staircase, so I've done some research. I'm amazed at how much contradicatory information there is online and how many conditions there are in the building regulations for this.

Disclaimer (to avoid legal repurcussions) - The figures I've used in these questions are based on various online sources. They are roughly accurate based on what I've seen, to provide real-life questions for students, but they shouldn't be used as guidance for building staircases.

 

Solutions

\(tan(pitch)=\frac{rise}{tread}\)

\(tan^{-1}(\frac{17}{29})=30.4^{\circ}\)

 \(\frac{14}{tan(28)}=26.3 cm\)

Solutions

A - No. \(22+2(16)=54<55\)

B - Yes

C - No. \(t=\frac{15}{tan(40)}=17.9<24.5\)

D - Yes

E - Yes

F - No. \(\frac{18.5}{tan(35)}=26.4>26\)

G - No. The tread is 28>26

H - No. \(24.5+2(15)=54.5<55\)

Solution

\(tan^{-1}(\frac{2.9}{3.7})=38.1^{\circ}\) which is less than 42, so yes.

Consider bounds.

For the rise:
\(\frac{290}{15}=19.33\) and \(\frac{290}{22}=13.18\)

For the tread:
\(\frac{370}{24.5}=11.02\) and \(\frac{370}{26}=14.23\)

The only integer (as we need an integer number of steps) that satisfies both conditions is 14.

And finally, a Desmos graph to demonstrate the scenario.