{"id":14399,"date":"2020-01-28T16:07:00","date_gmt":"2020-01-28T16:07:00","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=14399"},"modified":"2026-02-25T16:29:39","modified_gmt":"2026-02-25T16:29:39","slug":"dc-ec-07-reinforcement-in-beam-shear-and-torsion-uls-design","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/es\/knowledge-base\/dc-ec-07-reinforcement-in-beam-shear-and-torsion-uls-design\/","title":{"rendered":"DC EC 07: reinforcement in beam shear and torsion (ULS design)"},"content":{"rendered":"
Description<\/h2>\n
<\/p>\n
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\n\n
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Geometry<\/th>\n
Cross-section:<\/td>\n
\n<\/td>\n<\/tr>\n
\n
Material:<\/td>\n
C25\/30<\/td>\n<\/tr>\n
\n
Concrete cover:<\/td>\n
<\/td>\n<\/tr>\n
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Load<\/th>\n
Self-weight: \nDead loads:\u200c\u200d<\/p>\n
\n<\/td>\n
neglected \n at end of span \n at end of span<\/td>\n<\/tr>\n
\n
Internal forces<\/th>\n
<\/td>\n
\n \n<\/td>\n<\/tr>\n
\n
Standard<\/th>\n
<\/td>\n
EN 1992-1-1 [- -]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
Independent reference results<\/h2>\n
<\/span>Open handcalculations<\/div>
\n
The beam is subjected to a bending moment M, shear force V and torsion T.<\/p>\n
\n
The bending moment M will cause longitudinal reinforcement.<\/li>\n
The shear force V will cause transverse reinforcement. And, if the shear force is so high that stirrups under 45\u00b0 are required, also longitudinal web reinforcement (see DC EC 09<\/a>).<\/li>\n
![\"\"](\"https:\/\/support.buildsoft.eu\/wp-content\/uploads\/2025\/01\/DC-EC07a1.jpg\")
<\/p>\n![\"b=200mm\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-723638e85d37d6d2e7138132abd0290a_l3.png\" "\\"Rendered")
![\"h=400mm\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-041aa2d772dcd1ce8317c0835bc6ad14_l3.png\" "\\"Rendered")
<\/td>\n<\/tr>\n![\"c=40mm\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-2cd197ec94746bb0d09ed02eb9d8d829_l3.png\" "\\"Rendered")
<\/td>\n<\/tr>\n![\"P=30\text{kN}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-2c9d3b244b3f2c3d9e208c3d2e4e5529_l3.png\" "\\"Rendered")
at end of span![\"T=6\text{kNm}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-62d52c1d0d822846dd762b0ab2ab9240_l3.png\" "\\"Rendered")
at end of span<\/td>\n<\/tr>\n![\"M_{Ed.ULS}=162\text{kNm}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-f65a51a7c9f67ff277ee519d7deb69f6_l3.png\" "\\"Rendered")
![\"V_{Ed.ULS}=40.5\text{kN}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-24766e08603895b564fb954dd8cacf3c_l3.png\" "\\"Rendered")
![\"T_{Ed.ULS}=8.10\text{kNm}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-3c20feb8fbafd1cf72b5cd28d89be040_l3.png\" "\\"Rendered")
<\/td>\n<\/tr>\n![\"M_{Ed.ULS}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-24c13e235a8e8e1d3695075fc7d3f31d_l3.png\" "\\"Rendered")
<\/h3>\n![\"A_{y.M.top}=1304mm^2\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-560aac417740aac771f6f3d018176bcf_l3.png\" "\\"Rendered")
and ![\"A_{y.M.bottom}=144mm^2\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-2b378482eb33b01e37f99e88f5ec7474_l3.png\" "\\"Rendered")
<\/li>\n![\"A_{y.M.top}=A_{y.M.bottom}=107mm^2\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-6bf320b71d1b32890a15105567956835_l3.png\" "\\"Rendered")
.<\/li>\n<\/ul>\n![\"V_{Ed.ULS}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-a386b92dd41cfe2dccf24f10c5051da4_l3.png\" "\\"Rendered")
<\/h3>\n![\"A_{wz.V}=160mm^2/m\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-b91f063ccc41737e4faef9d7420df8d1_l3.png\" "\\"Rendered")
<\/li>\n![\"A_{wz.V}=173mm^2/m\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-120b8235fdf66fc42b4b2737cee6ff9d_l3.png\" "\\"Rendered")
.<\/li>\n<\/ul>\n![\"T_{Ed.ULS}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-6c2db45449adad94bdd14ca28dcda08a_l3.png\" "\\"Rendered")
<\/h3>\n![\"\[A = b \cdot h = 200mm \cdot 400mm=80000mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-1c280fe5743e4b1765dbd132cc86b6ad_l3.png\" "\\"Rendered")
<\/p>\n![\"\[u=2 \cdot \left ( b+h \right )=2 \cdot \left ( 200mm+400mm \right )=1200mm\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-3e120b2101aaf166ec1ac2340eafc469_l3.png\" "\\"Rendered")
<\/p>\n![\"\[t_{ef}=max\left (\frac{A}{u},2 \cdot c \right )= max\left (\frac{80000mm^2}{1200mm},2 \cdot 40mm \right )=80mm\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-215fe691398a53b39060a3f9c470f881_l3.png\" "\\"Rendered")
<\/p>\n![\"\[b_{ef}=b- t_{ef}= 200mm-80mm=120mm\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-6d329585752817f14b153797bc9aa50a_l3.png\" "\\"Rendered")
<\/p>\n![\"\[h_{ef}=h- t_{ef}= 400mm-80mm=320mm\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-f74456d8d8a461e0b248d1745d03de1c_l3.png\" "\\"Rendered")
<\/p>\n![\"\[A_k=b_{ef} \cdot h_{ef}= 120mm \cdot 320mm = 38400mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-7c6bdba8ce6e23b977431ec4e248acf9_l3.png\" "\\"Rendered")
<\/p>\n![\"\[T_{Rd.c}=f_{ctd} \cdot t_{ef} \cdot 2 \cdot A_k = 1.71\text{MPa} \cdot 80mm \cdot 2 \cdot 38400mm^2=10.51 \text{kNm}\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-0de93f847dabcf9b063e2d269d7c2c09_l3.png\" "\\"Rendered")
<\/p>\n![\"\[\frac{T_{Ed.ULS}}{T_{Rd.c}} +\frac{ V_{Ed.ULS} }{V_{Rd.c}} > 1 \Rightarrow \text{calculated reinforcement is required}\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-df10723940d48a395af719a84d2a2bf6_l3.png\" "\\"Rendered")
<\/p>\n![\"V_{Rd.c}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-3754887e1d417c5097fa47e2982c0c8a_l3.png\" "\\"Rendered")
was calculated in ![\"29.05\text{kN}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-56515e2f30f5bc27569ee25b721f2d23_l3.png\" "\\"Rendered")
.<\/p>\n![\"\[\nu =0.6 \cdot \left ( 1-\frac{f_{ck}}{250\text{MPa}} \right )=0.6 \cdot \left ( 1-\frac{25\text{MPa}}{250\text{MPa}} \right )=0.54\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-2d85d2666d9497e37b16a015dff7f6dc_l3.png\" "\\"Rendered")
<\/p>\n![\"\begin{align*}](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-dda3654ac5586bcc305ed962753100ed_l3.png\" "\\"Rendered")
<\/p>\n![\"\[\frac{T_{Ed.ULS}}{T_{Rd.max}} + \frac{V_{Ed.ULS}}{V_{Rd.max}} < 1 \Rightarrow \text{compression strut is OK}\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-9ec54c8c67606c3170532b59a3411fb3_l3.png\" "\\"Rendered")
<\/p>\n![\"V_{Rd.max}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-41ec75270b531c69adcf9c4b24f42425_l3.png\" "\\"Rendered")
was calculated in ![\"257.47\text{kN}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-ac4df14a2d266e3b42ea0a454af2a0a9_l3.png\" "\\"Rendered")
<\/p>\n![\"\frac{T_{Ed.ULS}}{T_{Rd.max}} + \frac{V_{Ed.ULS}}{V_{Rd.max}} >1\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-11416425785d6c1609d689be2e2519e9_l3.png\" "\\"Rendered")
, then the compression strut would be insufficient and you’d see a skull in Diamonds.<\/p>\n![\"\[u_k= 2 \cdot \left ( b_{ef} + h_{ef}\right )= 2 \cdot \left ( 120mm + 320mm\right )=880mm\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-5a526864456ec8a54e82a02017c2d8f7_l3.png\" "\\"Rendered")
<\/p>\n![\"\begin{align*}](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-ea62b30f3f1ce49e6e993586bf8f522e_l3.png\" "\\"Rendered")
<\/p>\n![\"A_{w.T}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-94d55c9980f8b71ce0350cd4d490b925_l3.png\" "\\"Rendered")
is the required cross-section of the stirrups on one side of the beam. But ![\"A_{wz}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-4dd4f7f4e4bc3b20b9ede0009da899e8_l3.png\" "\\"Rendered")
in Diamonds represent the cross-section of the stirrups on the left AND right side of the beam. Analogous for ![\"A_{wy}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-ae187225a6ece3d7c568f22a60b7d830_l3.png\" "\\"Rendered")
which represents the cross-section of the stirrups on the top AND bottom side of the beam. Therefor the result ![\"\[A_{wz.T}=A_{wy.T}=2 \cdot A_{w.T}=2 \cdot 146mm^2/m=292mm^2/m\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-e59a74cacf15f408406eb5f5500dd1bc_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n![\"\[A_{s.T}=\frac{T_{Ed.ULS} \cdot cot(\theta) \cdot u_k}{2 \cdot A_k \cdot f_{yd}}=\frac{8.1\text{kNm} \cdot cot(31^\circ) \cdot 880mm}{2 \cdot 38400mm^2 \cdot 434.7 \text{MPa}}=355mm^2 \]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-26e9c2590de9ae7070948fbca0a57d30_l3.png\" "\\"Rendered")
<\/p>\n![\"\begin{align*}](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-f01633718a93639317cb15e7044f0936_l3.png\" "\\"Rendered")
<\/p>\n![\"\begin{align*}](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-cbaec17f910ca5d50566089067745282_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n<\/ul>\n![\"\[A_{wz}=A_{wz.T}+A_{wz.V}=292mm^2/m+173mm^2/m=465mm^2/m\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-f1f08f34f98c365dd4e8d639d93d9dd0_l3.png\" "\\"Rendered")
<\/p>\n![\"\[A_{wy}=A_{wy.T}+A_{wz.V}=292mm^2/m+0mm^2/m=292mm^2/m\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-d531f07d8fb9c5174e2c22d5f73a3bd3_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n![\"A_{y.T}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-03544fa3a67422b8e3bc383f6ce68e97_l3.png\" "\\"Rendered")
is neglected because it’s smaller than the minimum reinforcement.<\/p>\n![\"\[A_{y.top}=A_{y.M.top}+A_{y.T}=107mm^2+0mm^2=107mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-a17a342fc40676de76da96bd45d268c3_l3.png\" "\\"Rendered")
<\/p>\n![\"\[A_{y.bottom}=A_{y.top}\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-0ea6298c397a4e3f635da8b042fc3515_l3.png\" "\\"Rendered")
<\/p>\n![\"A_{z.T}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-7893361949d5c5d7c2d74403f8d491ac_l3.png\" "\\"Rendered")
should be divided over the left and right side of the beam.<\/p>\n![\"\[A_{z.left}=A_{z.right}=\frac{A_{z.T}}{2}=129mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-1e932697326b77d745ce9bacaedb1508_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n<\/ul>\n![\"A_{wz.V}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-65b2fb57b439e35a0dbce8c30aaf90d3_l3.png\" "\\"Rendered")
equals the minimum shear reinforcement. It is neglected because ![\"A_{wz.T}\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-cb0cc63b69f16a4fda18ee8022ea6258_l3.png\" "\\"Rendered")
is larger.<\/p>\n![\"\[A_{wz}=A_{wz.T}+A_{wz.V}=292mm^2/m+0mm^2/m=292mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-f565975a83a825f22b38cfe5945476c0_l3.png\" "\\"Rendered")
<\/p>\n![\"\[A_{wy}=A_{wz}=292mm^2/m\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-87b32b04b46cb2d3dfa098c902d8a50c_l3.png\" "\\"Rendered")
<\/p>\n<\/li>\n![\"\[A_{y.top}=A_{y.M.top}+\frac{A_{y.T}}{2}=1304mm^2+48mm^2=1352mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-7bee68935ea730228ea7adc9f7bbe491_l3.png\" "\\"Rendered")
<\/p>\n![\"\[A_{y.bottom}=A_{y.M.bottom}+\frac{A_{y.T}}{2}=144mm^2+48mm^2=192mm^2\]\"](\"https:\/\/support.buildsoft.eu\/wp-content\/ql-cache\/quicklatex.com-ebf59dcdabb4d987ff61301baf9487f4_l3.png\" "\\"Rendered")
<\/p>\n![\"\"](\"https:\/\/support.buildsoft.eu\/wp-content\/uploads\/2025\/01\/DC-EC-07c.jpg\")
<\/p>\n