{"id":11510,"date":"2023-12-06T16:14:48","date_gmt":"2023-12-06T16:14:48","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=11510"},"modified":"2025-04-15T15:06:15","modified_gmt":"2025-04-15T15:06:15","slug":"dc-ec-02-longitudonal-reinforcement-in-beam-under-pure-bending","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/dc-ec-02-longitudonal-reinforcement-in-beam-under-pure-bending\/","title":{"rendered":"DC EC 02: longitudinal reinforcement in beam under pure bending (ULS FC design)"},"content":{"rendered":"

Description<\/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<\/td>\n<\/tr>\n
Concrete cover:<\/td>\n\"c=40mm\"<\/td>\n<\/tr>\n
Load<\/th>\nSelf-weight:
\nDead loads:<\/td>\n		neglected
\n\"P=15kN\" at end of span<\/td>\n<\/tr>\n
Internal forces<\/th>\n<\/td>\n\"M_{Ed.ULS}=81\text{kNm}\"<\/td>\n<\/tr>\n
Standard<\/th>\n<\/td>\nEN 1992-1-1 [- -] and [BE]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Independent reference results<\/h2>\n
<\/span>Handcalculation according to EN 1992-1-1 --<\/div>
\n

Required reinforcement:<\/p>\n

  <\/span>   <\/span>\"\[d=h-c=400mm-40mm=360mm\]\"<\/p>\n

  <\/span>   <\/span>\"\[\mu _d=\frac{M_{Ed.ULS}}{b\cdot d^2\cdot f_{cd}}=\frac{81\text{kNm}}{200mm\cdot (360mm)^2\cdot 16.7\text{MPa}}=0.190\]\"<\/p>\n

Table 3 from Gewapend beton: numeri<\/em> (click here to open<\/a> the Table) shows \"\omega _1\" as a function of \"\mu _d\", and we find:<\/p>\n

  <\/span>   <\/span>\"\[\omega _1=0.210\]\"<\/p>\n

  <\/span>   <\/span>\"\[A_{s1}=\omega _1 \cdot b\cdot d\cdot \frac{f_{cd}}{f_{yd}}=0.210 \cdot 200mm \cdot 360mm \cdot \frac{16.7\text{MPa}}{434.8\text{MPa}}=581mm^2\]\"<\/p>\n

Minimum reinforcement:<\/p>\n

(9.1N) <\/span>   <\/span>\"\begin{align*}<\/p>\n

Diamonds calculates the minimum reinforcement with \"h\" instead of \"d\" because for more complex cross-section shapes, \"d\" is not unambiguously defined. Therefor \"h\" is a safe alternative.<\/p>\n<\/div><\/div><\/div>\n

<\/span>Handcalculation according to EN 1992-1-1 BE<\/div>
\n

Required reinforcement:<\/p>\n

  <\/span>   <\/span>\"\[d=h-c=400mm-40mm=360mm\]\"<\/p>\n

  <\/span>   <\/span>\"\[\mu _d=\frac{M_{Ed.ULS}}{b\cdot d^2\cdot \alpha_{cc} \cdot f_{cd}}=\frac{81\text{kNm}}{200mm\cdot (360mm)^2\cdot 0.85 \cdot 16.7\text{MPa}}=0.216\]\"<\/p>\n

Table 3 from Gewapend beton: numeri<\/em> (click here to open<\/a> the Table) shows \"\omega _1\" as a function of \"\mu _d\".<\/p>\n

  <\/span>   <\/span>\"\[\omega _1=0.216\]\"<\/p>\n

  <\/span>   <\/span>\"\[A_{s1}=\omega _1 \cdot b\cdot d\cdot \frac{\alpha_{cc} \cdot f_{cd}}{f_{yd}}=0.216 \cdot 200mm \cdot 360mm \cdot \frac{0.85 \cdot16.7\text{MPa}}{434.8\text{MPa}}=595mm^2\]\"<\/p>\n

Minimum reinforcement:<\/p>\n

(9.1N) <\/span>   <\/span>\"\begin{align*}<\/p>\n

Diamonds calculates the minimum reinforcement with \"h\" instead of \"d\" because for more complex cross-section shapes, \"d\" is not unambiguously defined. Therefor \"h\" is a safe alternative.<\/p>\n<\/div><\/div><\/div>\n

Diamonds results and comparison<\/h2>\n

According to EN 1992-1-1 [- -]<\/h4>\n

\"\"<\/p>\n

Longitudinal reinforcement calculated by Diamonds (EN 1992-1-1 [- -])<\/strong><\/p>\n

\n\n\n\n\n\n
Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
Maximum longitudinal reinforcement<\/td>\n765 mm\u00b2<\/td>\n768 mm\u00b2<\/td>\n-0,45%<\/td>\n<\/tr>\n
Minimum longitudinal reinforcement<\/td>\n107 mm\u00b2<\/td>\n107 mm\u00b2<\/td>\n0,00%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

According to EN 1992-1-1 [BE]\"\"<\/h4>\n

Longitudinal reinforcement calculated by Diamonds (EN 1992-1-1 [BE])<\/strong><\/p>\n

\n\n\n\n\n\n
Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
Maximum longitudinal reinforcement<\/td>\n798 mm\u00b2<\/td>\n798 mm\u00b2<\/td>\n0,00%<\/td>\n<\/tr>\n
Minimum longitudinal reinforcement<\/td>\n107 mm\u00b2<\/td>\n107 mm\u00b2<\/td>\n0,00%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n