Part 2, Section 3.8.3 Assessment of Crack Widths

Un-tensioned reinforcement is added to ensure that the reinforcement stresses remain below 0.8f_y.

Crack widths are calculated per BS 8110 Part 2, equation 12. A concrete stress strain curve that approximates tension stiffening is used - see Concrete Behavior . Creep is not considered.

Un-tensioned reinforcement is added to keep crack widths at or below 0.3mm (per 3.2.4.2).

This criterion is applied to two-way slabs, but equation 12 will not provide accurate crack width predictions for two way slabs when wide design strip segments or wide design sections are used.

The crack-limiting capabilities of appropriately placed bonded post-tensioning tendons are considered, and the balance loading will be considered if included in the load combinations.

In determining the effectiveness of bonded tendons, equation 12 can be manipulated as follows:

Crack width = (3a_crε_m ) / [1+2(a_cr - c_min) / (h-x)]

= ε_ms_c
s_c = 3a_cr / [1+2(a_cr - c_min) / (h-x)] = crack spacing

RAM Concept assumes the maximum crack spacing is 3(h-x).

RAM Concept assumes that each bar and bonded tendon is placed horizontally to give the same crack spacing. Bars and tendons that - due to their elevation - cannot provide the crack spacing are ignored.

s_c = 3a_cr / [1+2(a_cr - c_min) / h_t]

where

h_t

(h-x) = height of tension zone

s_c = 3a_cr h_t / [h_t +2(a_cr - c_min) ]

s_c [h_t +2(a_cr - c_min) ] = 3a_cr h_t

s_c h_t +2s_ca_cr - 2s_cc_min = 3a_cr h_t

s_c h_t - 2s_cc_min = 3a_cr h_t - 2s_ca_cr

s_c h_t - 2s_cc_min = a_cr (3h_t - 2s_c)

a_cr = (s_c h_t - 2s_cc_min) / (3h_t - 2s_c)

However, $a_{c r} = \sqrt{s_{b}^{2} + c_{\min}^{2}}$ , where s_b = half the horizontal spacing between reinforcement

\sqrt{s_{b}^{2} + c_{\min}^{2}} = (s_{c} h_{t} - 2 s_{c} c_{\min}) / (3 h_{t} - 2 s_{c})

Rearranging and solving for s_b produces:

s_{b} = \sqrt{{(s_{c} h_{t} - 2 s_{c} c_{\min})}^{2} / {(3 h_{t} - 2 s_{c})}^{2} - c_{\min}^{2}}

Using this final equation, RAM Concept determines a spacing for each bar or bonded tendon that is effective in controlling cracking. RAM Concept iteratively determines the s_c that gives the s_bs that sum to the tension face width.

For bonded tendons, the cover c_min is assumed to be the cover to the centroid of the tendon, and the "bar" diameter is assumed to be zero. Both of these assumptions are conservative.