The concept of loading balancing is useful in selecting tendon profile, which can supply most desirable system of forces in concrete, straight portion of cable profile does not produce any reactions at end, while curve and sharp angles of cable develop uniformly distributed and concentrated load respectively.

The shift of pressure line is measured from centroidal axis is obtained as
E?= (a-e) = (m/p)-e, basically load carrying mechanism is comprised of a constant force with a changing lever arm as in case of prestressed concrete sections, and a changing force with a constant lever arm prevailing in reinforced concrete sections.

P = 180kn, A = 36�10³mm², e = 50mm, b = 120mm, d = 300mm, z = 18�10⁵mm³
Stresses due to prestress = (p/a) = (180�10³/36�10³) = 5n/mm², (p_e/z) = (180�10³�50/18�10⁵) = 5n/mm² Total stress = ((p/a)+(p_e/z))=(5+5) = 10n/mm².

m/z = 5.74, b = 250mm, d = 600mm
Z = (250�600²/6) = 15�10⁶mm³,
M = (5.74�15�10⁶) = 86.1�10⁶nmm = 86.1knm.

The stresses developed at top and bottom fibers of beam are obtained by two relations:
F_inf = (p/a+p_e/z_b) = p/a(1+ey_b/i²), F_sup = (p/a-p_e/z_b) = p/a(1-y_bt/i²).

In case of prestressed concrete members, location of pressure line depends upon magnitude and direction of moments applied at cross section and magnitude and distribution of stresses due to prestressing force, increase in resultant forces are due to a more or less constant lever arm between forces, characterized by properties of composite section.

The stresses in tendons of bonded beams is ?_e (My/I), ?_e = Modular ratio of steel to concrete, y = vertical distance of a point from centroid of concrete section, M = bending moment, I = moment of area of section, in cases of bonded members such as pretensioned elements or post tensioned grouted members, composite action between steel and concrete prevails and stresses in steel are computed using ory of composite sections up to stage of cracking.

Moment of area I = (100�300³/12) = 225�10⁶mm⁴
Prestressing force p = (1000�100) = 10⁵ = 100kn
Rotation due to prestressing force ?_p = PeL/2EI = (100�50�6�10³/2�36�225�10⁶)
Hogging moment = 0.00185radians.

b=150mm, d=300mm, l = 10m, e=50mm, p=500kn
Self weight of beam g = (0.15�0.3�24)=1.08kn/m,
Moment due to self weight = (0.125�1.08�10²=13.5knm,
Stress due to self weight = (13.5�10⁶/225�10⁴) = 6n/mm²,
Stress due to prestressing = (P/A+Pe/A) = (500�10³/45�10³)+(500�10³�50/225�10⁴) = 22.22n/mm².

If M_q and M_g are live loads and dead load moments at central span section;
M_q=ql²/8
M_g=gl²/8