I believe that you may be asking for the impossible in aiming for "insignificant" inbuilt stresses.  It depends very much what you consider to be "insignificant".

Common practice would be to cast your section in two pours, with construction joints close to the top of the webs.

If you cannot cast each section in one continuous pour, then it would keep your inbuilt stresses down if you cast the ends prior to casting the midspan portion.

Estimating the inbuilt stresses is not all that difficult, provided that you can assess the stiffness of each previously cast section of the girder at the time of each new pour.

Just calculate the bending moments due to each new pour, and distribute them between the supporting truss and any previously cast concrete in proportion to the relative flexural stiffnesses.

That is, the bending moment in the concrete at any location Mconc = Mtotal * (Econc*Iconc)/(Etruss*Itruss + Econc*Iconc).

Then apply Mconc to the concrete section to determine the stresses you are looking for.

This appears to be an extension of a previous thread.

My suggestion would be to concrete the central 50% or more of the
span in the first pour, and then the ends. This way, the scaffolding
would see the maximum central loading and achieve most of the
deflection when the central portion of the concrete is green. This part
of the concrete is not stressed. The ends are cast later. The load
at the ends would not result in high central deflection. Since the
concrete is green at the ends, it would take the shape of the
deflected scaffolding without inducing any stress in that region. The
central portion would be subject to only a small additional deflection,
and the stresses would be quite small.

The formula suggested by austim would be valid if the span is
concreted in multiple pours in horizontal layers. For concreting the
way mentioned above, that would not be applicable. Assuming that the
central part would have set by the time the ends are concreted, the
following course of action is to be followed:

(a) Assume that the concrete girder is only supported at the ends of
the first pour. Compute the self-weight deflection at the centre. Compute
the additional deflection of the truss scaffolding due to the weight of the
concrete (relative deflection between support point mentioned above
and centre of the span). If the girder deflection is more than the truss
deflection, the truss supports the girder. Otherwise the girder is
supported only at ends.
(b) Find the compatible deflection pattern of the girder and truss. From
the deflection pattern, the bending moment and stresses can be
computed.

This is a convoluted and iterative procedure. May be one trial would
lead to a conclusion that the additional stresses are not critical.

Good luck,

M. Hariharan