{"id":13527,"date":"2024-09-12T12:16:07","date_gmt":"2024-09-12T12:16:07","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=13527"},"modified":"2026-01-20T15:03:17","modified_gmt":"2026-01-20T15:03:17","slug":"dc-ec-10-stress-limites-in-beam-under-pure-bending-sls-design","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/nl\/knowledge-base\/dc-ec-10-stress-limites-in-beam-under-pure-bending-sls-design\/","title":{"rendered":"DC EC 10: stress limites in beam under pure bending (SLS design)"},"content":{"rendered":"

Description
\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
Reinforcement required for ULS:<\/td>\n\"A_{s1.ULS}=1189mm^2\"
\n\"A_{s2.ULS}=107mm^2\"<\/td>\n<\/tr>\n
Creep factor:<\/td>\n\"\phi_{stress}=1.36\"<\/td>\n<\/tr>\n
Loads<\/th>\n<\/td>\n\"M_{Ed.SLS.RC}=144.9\text{kNm}\"
\n\"M_{Ed.SLS.RC}=104\text{kNm}\"
\n\"M_{Ed.SLS.QP}=83\text{kNm}\"<\/td>\n<\/tr>\n
Standard<\/th>\n<\/td>\nEN 1992-1-1 [- -]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\nNote: this model is similar to DC EC 04<\/a> and DC EC 08<\/a>, but we’ve increased the loads so the additional reinforcement due to the stress limits would be clearly present.<\/p>\n

Independent reference results<\/h2>\n
<\/span>Open handcalculations<\/div>
\n

Determine the limits for the allowable stresses (EN 1992-1-1)<\/h4>\n
    \n
  • Maximum allowable concrete stress in SLS RC\n

      <\/span>   <\/span>\"\[\sigma_{c.RC.max}=0.6 \cdot f_{ck}= 0.6 \cdot 25 \text{MPa}= 15\text{MPa}\]\"<\/p>\n<\/li>\n

  • Maximum allowable concrete stress in SLS QP\n

      <\/span>   <\/span>\"\[\sigma_{c.QP.max}=0.45 \cdot f_{ck}= 0.45 \cdot 25 \text{MPa}= 11.25\text{MPa}\]\"<\/p>\n<\/li>\n

  • Maximum allowable steel stress in SLS RC\n

      <\/span>   <\/span>\"\[\sigma_{s.RC.max}=0.8 \cdot f_{yk}= 0.8 \cdot 500 \text{MPa}= 400\text{MPa}\]\"<\/p>\n<\/li>\n<\/ul>\n

    Verify the concrete and steel stresses with ULS<\/h4>\n

    Determine cracked moment of inertia (creep, theoretical ULS reinforcement)<\/h5>\n

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

      <\/span>   <\/span>\"\[\alpha_{cr}=\frac{E_s}{\frac{E_c}{1+\phi_{stress}}}=15\]\"<\/p>\n

      <\/span>   <\/span>\"\[x_{cr.ULS}=175.6mm\]\"<\/p>\n

      <\/span>   <\/span>\"\[I_{cr.ULS}=\frac{b \cdot x_{cr.ULS}^3}{3}+(\alpha_{cr}-1) \cdot A_{s2.ULS} \cdot (x_{cr.ULS}-d_2)^2 + \alpha_{cr} \cdot A_{s1.ULS} \cdot (d-x_{cr.ULS})^2\]\"<\/p>\n

      <\/span>   <\/span>\"\[I_{cr.ULS}=995 \cdot 10^6 mm^4\]\"<\/p>\n

    Determine concrete and steel stresses<\/h5>\n
      \n
    • Concrete stress in SLS RC\n

        <\/span>   <\/span>\"\[\sigma_{c.RC}=\frac{M_{Ed.SLS RC} \cdot x_{c.ULS}}{I_{cr.ULS}} = \frac{104 \text{kNm} \cdot 175.6mm}{995 \cdot 10^6 mm^4}=18.36\text{MPa}\]\"<\/p>\n<\/li>\n

    • Concrete stress in SLS QP\n

        <\/span>   <\/span>\"\[\sigma_{c.QP}=\frac{M_{Ed.SLS QP} \cdot x_{c.ULS}}{I_{cr.ULS}} = \frac{83 \text{kNm} \cdot 175.6mm}{995 \cdot 10^6 mm^4}=14.65\text{MPa}\]\"<\/p>\n<\/li>\n

    • Steel stress in SLS RC\n

        <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/li>\n<\/ul>\n

      Compare<\/h5>\n
        \n
      • Concrete stress in SLS RC\n

          <\/span>   <\/span>\"\[\sigma_{c.RC} > \sigma_{c.RC.max}\]\"<\/p>\n

          <\/span>   <\/span>\"\[18.36\text{MPa} > 15\text{MPa} \Rightarrow \text{NOT OK}\]\"<\/p>\n<\/li>\n

      • Concrete stress in SLS QP\n

          <\/span>   <\/span>\"\[\sigma_{c.QP} > \sigma_{c.QP.max}\]\"<\/p>\n

          <\/span>   <\/span>\"\[14.65\text{MPa} >11.25\text{MPa} \Rightarrow \text{NOT OK}\]\"<\/p>\n<\/li>\n

      • Steel stress in SLS RC\n

          <\/span>   <\/span>\"\[\sigma_{s.RC} \le \sigma_{s.RC.max}\]\"<\/p>\n

          <\/span>   <\/span>\"\[289.07 \text{MPa} \le 400\text{MPa} \Rightarrow \text{OK}\]\"<\/p>\n<\/li>\n<\/ul>\n

        The concrete stresses in SLS RC and QP are too high. So Diamonds will add upper and lower reinforcement until the requirements are met. Diamonds finally suggests \"592mm^2\" upper and \"1538mm^2\" lower reinforcement. Let’s see if the stress limits are met with these reinforcement amounts.<\/p>\n

        Verify the concrete and steel stresses with ULS + SLS reinforcement<\/h4>\n

        Determine cracked moment of inertia (creep, theoretical ULS + SLS reinforcement)<\/h5>\n

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

          <\/span>   <\/span>\"\[\alpha_{cr}=\frac{E_s}{\frac{E_c}{1+\phi_{stress}}}=15\]\"<\/p>\n

          <\/span>   <\/span>\"\[x_{cr.SLS}=176.2mm\]\"<\/p>\n

          <\/span>   <\/span>\"\[I_{cr.SLS}=\frac{b \cdot x_{cr.SLS}^3}{3}+(\alpha_{cr}-1) \cdot A_{s2.SLS} \cdot (x_{cr.SLS}-d_2)^2 + \alpha_{cr} \cdot A_{s1.SLS} \cdot (d-x_{cr.SLS})^2\]\"<\/p>\n

          <\/span>   <\/span>\"\[I_{cr.SLS}=1300 \cdot 10^6 mm^4\]\"<\/p>\n

        Determine concrete and steel stresses<\/h5>\n
          \n
        • Concrete stress in SLS RC\n

            <\/span>   <\/span>\"\[\sigma_{c.RC}=\frac{M_{Ed.SLS RC} \cdot x_{c.SLS}}{I_{cr.SLS}} = \frac{104 \text{kNm} \cdot 176.2mm}{1300 \cdot 10^6 mm^4}=14.09\text{MPa}\]\"<\/p>\n<\/li>\n

        • Concrete stress in SLS QP\n

            <\/span>   <\/span>\"\[\sigma_{c.QP}=\frac{M_{Ed.SLS QP} \cdot x_{c.SLS}}{I_{cr.SLS}} = \frac{83 \text{kNm} \cdot 176.2mm}{1300 \cdot 10^6 mm^4}=11.25\text{MPa}\]\"<\/p>\n<\/li>\n

        • Steel stress in SLS RC\n

            <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/li>\n<\/ul>\n

          Compare<\/h5>\n
            \n
          • Concrete stress in SLS RC\n

              <\/span>   <\/span>\"\[\sigma_{c.RC} \le \sigma_{c.RC.max}\]\"<\/p>\n

              <\/span>   <\/span>\"\[14.09\text{MPa} \le 15\text{MPa} \Rightarrow \text{OK}\]\"<\/p>\n<\/li>\n

          • Concrete stress in SLS QP\n

              <\/span>   <\/span>\"\[\sigma_{c.QP} \le \sigma_{c.QP.max}\]\"<\/p>\n

              <\/span>   <\/span>\"\[11.25\text{MPa} \le11.25\text{MPa} \Rightarrow \text{OK}\]\"<\/p>\n<\/li>\n

          • Steel stress in SLS RC\n

              <\/span>   <\/span>\"\[\sigma_{s.RC} \le \sigma_{s.RC.max}\]\"<\/p>\n

              <\/span>   <\/span>\"\[220.49 \text{MPa} \le 400\text{MPa} \Rightarrow \text{OK}\]\"<\/p>\n<\/li>\n<\/ul>\n<\/div><\/div><\/div>\n

            Diamonds results and comparison<\/h2>\n

            It is impossible to display the concrete and steel stresses in Diamonds. The only stresses displayed by Diamonds, are elastic stresses.<\/p>\n

            But from the calculate above, we can conclude that Diamonds verifies the stresses in a correct way. If you’d do the same calculation but lower \"A_{s1}\" and \"A_{s2}\" with \"2mm^2\", the concrete stresses in SLS QP would exceed again.<\/p>\n

            \"\"<\/p>\n

            Detailed result of the reinforcement calculated by Diamonds (EN 1992-1-1 [- -]).
            \nThe thin line is the reinforcement required to meet the ULS requirements, the thick is the reinforcement required to meet the ULS and SLS (stress) requirements.<\/strong><\/p>\n

            \n\n\n\n\n
            Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
            SLS reinforcement<\/td>\n592 mm\u00b2
            \n1538 mm\u00b2<\/td>\n            		592 mm\u00b2
            \n1538 mm\u00b2<\/td>\n            		0%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

            References<\/h2>\n
              \n
            • EN 1992-1-1: 2005 + AC: 2010<\/li>\n<\/ul>\n
                \n
              • Tested in Diamonds 2026.<\/li>\n<\/ul>\n\n","protected":false},"excerpt":{"rendered":"

                Description Note: this model is similar to DC EC 04 and DC EC 08, but we’ve increased the loads so the additional reinforcement due to the stress limits would be clearly present. Independent reference results Diamonds results and comparison It is impossible to display the concrete and steel stresses in…<\/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\/nl\/wp-json\/wp\/v2\/ht-kb\/13527"}],"collection":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb"}],"about":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/types\/ht_kb"}],"author":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/comments?post=13527"}],"version-history":[{"count":2,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/13527\/revisions"}],"predecessor-version":[{"id":23876,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb\/13527\/revisions\/23876"}],"wp:attachment":[{"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/media?parent=13527"}],"wp:term":[{"taxonomy":"ht_kb_category","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb-category?post=13527"},{"taxonomy":"ht_kb_tag","embeddable":true,"href":"https:\/\/support.buildsoft.eu\/nl\/wp-json\/wp\/v2\/ht-kb-tag?post=13527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}