{"id":13469,"date":"2024-07-09T13:36:01","date_gmt":"2024-07-09T13:36:01","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=13469"},"modified":"2025-07-16T10:07:20","modified_gmt":"2025-07-16T10:07:20","slug":"dc-ec-08-cracking-widths-in-beam-under-pure-bending-sls-design","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/dc-ec-08-cracking-widths-in-beam-under-pure-bending-sls-design\/","title":{"rendered":"DC EC 08: cracking widths in beam under pure bending (SLS design)"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/h2>\n
\n\n\n\n\n\n\n\n\n\n
Geometry<\/th>\nCross-section:<\/td>\n\"b=200mm\"
\n\"h=400mm\"<\/td>\n<\/tr>\n
Material:<\/td>\nC25\/30
\n\"E_c=31475\text{MPa}\"
\n\"E_s=200000\text{MPa}\"<\/td>\n<\/tr>\n
Concrete cover:<\/td>\n\"c=40mm\"<\/td>\n<\/tr>\n
Practical reinforcement:<\/td>\n\"A_{s1}=798mm^2\" divided over 2 bars
\n\"A_{s2}=107mm^2\" divided over 2 bars<\/td>\n<\/tr>\n
Creep factors:<\/td>\n\"\phi_{deformation}=2\"
\n\"\phi_{stress}=1.36\"<\/td>\n<\/tr>\n
Loads<\/th>\n<\/td>\n\"M_{Ed.SLS.RC}=74\text{kNm}\"
\n\"M_{Ed.SLS.QP}=60\text{kNm}\"<\/td>\n<\/tr>\n
Standard<\/th>\n<\/td>\nEN 1992-1-1 [- -]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Independent reference results<\/h2>\n
<\/span>Open handcalculations<\/div>
\n
    \n
  • Determine mean bar diameter\n

      <\/span>   <\/span>\"\[\phi_1=\sqrt{\frac{4 \cdot A_{s1.pr}}{\text{#}_{bars} \cdot \pi}}=\sqrt{\frac{4 \cdot 798mm^2}{2 \cdot \pi}}=22.54mm\]\"<\/p>\n

      <\/span>   <\/span>\"\[\phi_2=\sqrt{\frac{4 \cdot A_{s2.pr}}{\text{#}_{bars} \cdot \pi}}=\sqrt{\frac{4 \cdot 107mm^2}{2 \cdot \pi}}=8.25mm\]\"<\/p>\n<\/li>\n

  • Determine position of neutral line \"x_{cr}\"\n

      <\/span>   <\/span>\"\[0.5\cdot b\cdot x_{cr}^{2}+\left ( \alpha _{cr}-1 \right )\cdot A_{s2}\cdot \left (x_{cr}-d_2 \right )=\alpha_{cr} \cdot A_{s1}\cdot \left ( d-x_{cr} \right )\]\"<\/p>\n

      <\/span>   <\/span>\"\[\alpha_{cr}=\frac{E_s}{E_{cr.\infty}}=\frac{E_s}{\frac{E_c}{1+\phi}}=\frac{20 000 \text{MPa}}{\frac{31475\text{MPa}}{1+2}}=19.06\]\"<\/p>\n

      <\/span>   <\/span>\"\[x_{cr}=165mm\]\"<\/p>\n<\/li>\n

  • Determine maximum cracking distance \"s_{r1.max}\"\n

      <\/span>   <\/span>\"\[h_{eff}=min\left( 2.5 \cdot \left( h-d \right),\frac{h-x_{cr}}{3},\frac{h}{2} \right)=78.32mm\]\"<\/p>\n

      <\/span>   <\/span>\"\[A_{c.eff}=b \cdot h_{eff}= 15664mm^2\]\"<\/p>\n

      <\/span>   <\/span>\"\[\rho_{pr.eff}=\frac{A_{s1.pr}}{A_{c.eff}}=0.051\]\"<\/p>\n

      <\/span>   <\/span>\"\[k_1=0.8; k_2=0.5; k_3=3.4; k_4=0.425\]\"<\/p>\n

      <\/span>   <\/span>\"\[s_{r1.max}=\left( d_1 - \frac{\phi_1}{2}\right) \cdot k_3 + \frac{k_1 \cdot k_2 \cdot k_4 \cdot \phi_1}{\rho_{pr.eff}} = 172.9mm\]\"<\/p>\n<\/li>\n

  • Determine stress in tensile reinforcement
    \nFrom<\/p>\n

      <\/span>   <\/span>\"\[M_{Ed.SLS.QP}=(b \cdot x_{cr}-A_{s2})\cdot 0.5 \cdot \varepsilon_c\cdot\frac{E_c}{1+\phi_{stress}}\cdot \left( d-\frac{x_{cr}}{3}\right) + A_{s2} \cdot \varepsilon_{s2} \cdot E_s \cdot \left( d-d_2 \right)\]\"<\/p>\n

    And<\/p>\n

      <\/span>   <\/span>\"\[\varepsilon_c= \frac{\varepsilon_{s2} \cdot x_{cr}}{x_{cr}-d_2}\]\"<\/p>\n

    The value of \"\varepsilon_c\" can be deducted, namely 0.0008969.
    \nWhich can then be used to calculate the strain and stress in the tensile reinforcement<\/p>\n

      <\/span>   <\/span>\"\[\varepsilon_{s1}=\frac{\varepsilon_c \cdot \left( d-x_{cr} \right)}{x_{cr}}=0.001059\]\"<\/p>\n

      <\/span>   <\/span>\"\[\sigma_{s1}=\varepsilon_{s1} \cdot E_s=211.89MPa\]\"<\/p>\n

      <\/span>   <\/span>\"\[k_t=0.4\]\"<\/p>\n

      <\/span>   <\/span>\"\[\varepsilon_{sm}-\varepsilon_{cm}=max\left( \frac{\sigma_{s1}-k_t \cdot \frac{f_{ctm}}{\rho_{pr.eff}}\cdot \left( 1-\alpha_{cr} \cdot \rho_{pr.eff} \right)}{E_s}, 0.6 \cdot \frac{\sigma_{s1}}{E_s} \right) = 0.00106\]\"<\/p>\n<\/li>\n

  • Determine cracking width\n

      <\/span>   <\/span>\"\[w_k=s_{r1.max} \cdot \left( \varepsilon_{sm}-\varepsilon_{cm} \right)= 172.9mm \cdot 0.00106=0.183mm\]\"<\/p>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div>\n

    Diamonds results and comparison<\/h2>\n

    \"\"<\/p>\n

    Cracking width in a SLS QP combination calculated by Diamonds (EN 1992-1-1 [- -])<\/strong><\/p>\n

    \n\n\n\n\n
    Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
    Cracking width SLS QP<\/td>\n0.183mm<\/td>\n\u00a00.185mm<\/td>\n1.27%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    References<\/h2>\n
      \n
    • EN 1992-1-1: 2005 + AC: 2010<\/li>\n
    • Bhatt, P., MacGinley, T., & Choo, B. S. (2014). Reinforced Concrete Design to Eurocodes: Design Theory and Examples, Fourth Edition<\/i>. CRC Press.<\/li>\n<\/ul>\n
        \n
      • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n","protected":false},"excerpt":{"rendered":"

        Description Independent reference results Diamonds results and comparison Cracking width in a SLS QP combination calculated by Diamonds (EN 1992-1-1 [- -]) References EN 1992-1-1: 2005 + AC: 2010 Bhatt, P., MacGinley, T., & Choo, B. S. (2014). Reinforced Concrete Design to Eurocodes: Design Theory and Examples, Fourth Edition. CRC…<\/p>\n","protected":false},"author":3,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":[],"ht-kb-category":[1213],"ht-kb-tag":[],"_links":{"self":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/13469"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/comments?post=13469"}],"version-history":[{"count":3,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/13469\/revisions"}],"predecessor-version":[{"id":15432,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb\/13469\/revisions\/15432"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/media?parent=13469"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-category?post=13469"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/es\/wp-json\/wp\/v2\/ht-kb-tag?post=13469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}