Question

how to mark the centre of a beam using theodolite

Answer 1

Set up the theodolite anywhere you wish, making sure both ends and the centre of the beam are visible.
Take measurements of each end of the beam, both at the same height.
Determine the horizontal distance and horizontal angles.
Solve the triangle, and calculate the angle of the median makes with one end of the beam.
Set the the theodolite for this angle and mark accordingly.