Design for serviceability - preliminary design

what is the first objective of preliminary design for serviceability?

approximation to cross-sectional dimensions and effective prestress

how do we approximate depth of a beam if span < 36m

h(m) = span/25 + 0.1

how do we approximate depth of a beam if span >36m?

h(m) = span/20

what 2 assumptions are made when approximating effective prestress at midspan?

• usually lever arm is between 0.5h and 0.8h → a=0.6h

• if self-weight represents 50-60% of M_serv then M_sw = 0.5M_serv

based on assumptions how can effective prestress be approximated?

P_e 0.6 h = M_serv

what is P_e approximately for a rectangular section?

1700 h³ kN

how is minimum cross-sectional area determined?

assume average compressive stress in service at 20% of concrete compressive strength,

C=0.2f_cdA_c, T=P_e

P_e=0.2f_cdA_c=0.2(f_ck/1.5)A_c

A_c=P_e/(0.13f_ck)

if approximate effective stress at midspan is 1700h³kN, what is minimum cross-sectional area?

A_c,min = (1.7×10⁶ h³)/0.13f_ck= 1.3 × 10⁷ h³/f_ck

when can you use the effective prestress and minimum area approximations?

only for first estimates

how is initial prestressing force at transfer calculated?

P₀=P_jack - ΔP_i = 0.8-0.95P_jack

what actions are included when calculating prestressing force at transfer

self-weight only with partial safety factor

what are the allowable stresses in the concrete at transfer?

• top fibre - no tension allowed

• bottom fibre - compression limited to 60% of characteristic strength at age of transfer

how is effective prestressing force in service calculated?

P = P_jack - ΔP_i - ΔP_c+s+r

what combination of actions are included when calculating effective prestressing force in service?

self-weight + dead loads + live loads

what are the allowable stresses in the concrete when in service?

• in compression - limited to 45% of the characteristic compressive concrete strength

• in tension - not allowed