This nominal 1inch pipe - if you told me its actual dimension - two of
three of inner dia, wall thk., outer diameter - or what "Schedule" of
1inch pipe so I can look it up - I'd run the Euler-Bernoulli beam
calculation on it.
You could do Euler-Bernoulli - the familiar beam calc. yourself

Second Moment of Area
v
Section modulus
v
Section Moment capacity
v
Load-bearing capacity

You could also get the expected deflection - which can be had when you
know the Second Moment of Area.

Rich Smith