Theory and design of Structures

✔️Basic anchorage length ES EN 1992-1-1:2015 gives the following equation to determine the basic anchorage length, lb,req=(φ/4)(σₛ/fbd) where ✅σsd is the design stress of the bar at the position from where the anchorage is measured. ✅φ is diameter of bar ✅fbd=2.25η₁η₂fctd (eqn. 8.2) ✅fctd is the design value of concrete tensile strength. ✅η₁ is the coefficient related to the quality of the bond condition and the position of the bar during concreting 👉η₁=1 when 'good' conditions are obtained and 👉η₁=0.7 for all other cases ✅η₂ is related to the bar diameter 👉η₂ =1 for φ<= 32 mm 👉η₂=[132-φ]/100 for φ> 32 mm @theoryanddesignofstructures @Cengtalk_bot

K value in this table has a miss placed dot. And it should be 👉Simply supported:- 1.1 👉End span:- 1.13 👉Interior span:- 1.15 👉Slab supported on column( flat slab) :- 1.12 👉Cantilever:- 0.4 @theoryanddesignofstructures @Cengtalk_bot

Table 7.4N

7.16 a

✔️ depth from deflection ✅The limit states of deformation may be checked by either 👉by limiting the span/depth ratio(1). 👉by comparison a calculated deflection with a limit value(2). 🔑If method 1 is used , ES EN ON article 7.4.2 states that " it isn't necessary to calculate the deflections explicitly as simple rule, provided the limit to span/depth ratio formulated are satisfied." 🔑Equations 7.16 a and 7.16 b may be used to evaluate the limiting span to depth ratio. Both equations are shown in picture with caption 7.16 a. 🔑The limiting span / depth ratio for for concrete grade C30/37 and σs=310( fyk=500 Mpa) is evaluated based on the above two equations and is given th table 7.4N( picture with caption table 7.4N). @theoryanddesignofstructures @Cengtalk_bot

✔️Limiting depth of neutral axis(Xᵤ) to effective depth(d) ratio. ⭕️This discussion is limited to the case of fck<= 50 Mpa. From ES EN 1992-1-1:2015 Equation 5.10 a 🔑 δ=k₁+k₂Xᵤ/d for fcₖ<=50 Mpa Where:- ✅δ is the ratio of the redistributed moment to the elastic bending moment. 🔑And the national annex of Ethiopia recommendeds the following value for k₁ and k₂. K₁=0.44 K₂=1.25(0.6+0.0014/εcᵤ₂) From table 3.1 the value of εcᵤ₂ is 3.5 per thousand. Substituting into K₂ 🔑K₂=1.25(0.6+0.0014/(3.5/1000))=1.25 And for zero percent redistribution the value of δ=1 Now, the value of xu/d becomes 🔑Xu/d = (1-0.44)/1.25= 0.448 For a member subjected to flexure, if xu/d is less than 0.447 the section can be designed as singly reinforced. ✅This value is the same for EBCS -2-1995 @theoryanddesignofstructures @Cengtalk_bot

value of a cont.

value of a

Effective Span of beams and slabs in buildings[ ES EN 1992-1-1: 2015 Article 5.3.2.2]. The effective span , lₑff, of a member should be calculated as follows:- lₑₗₗ=lₙ+a₁+a₂ where:- lₙ is the clear distance between the faces of the supports. for values of a₁ and a₂ see the pictures with caption 'value of a'. @Cengtalk_bot

Class

Cₘᵢₙ,dur

Table 4.2

Cover continued 🔑ΔCdev the recommended national annex Value is 10 mm. ✅Now the equation for cover simplifies to: 🔑Cₘᵢₙ= max {Cₘᵢₙ,b ; Cₘᵢₙ,dᵤᵣ; 10 mm } 🔑Cₙₒₘ=Cₘᵢₙ +10 @theoryanddesignofstructures

Cover Continued 👉Cmin,b Minimum cover due to bond requirement 👉Cmin,dur minimum cover due to environmental conditions 👉ΔCdᵤᵣ,γ additive safety element 👉ΔCdᵤᵣ,st reduction of minimum cover for use of stainless steel 👉ΔCdᵤᵣ,add reduction of minimum cover for use of additional protection. 🔑According to table 4.2 of ES EN 1992-1-1:2015 the minimum cover, Cmin,b depends on the arrangement of bars and the maximum aggregate size( see the picture with caption ' table 4.2 '). 🔑Cmin,dur depends on structural classification( picture with caption class) given in table 4.2N of the code. and the Cmin,dur is given in the picture with caption 'Cmin,dur'. 🔑ΔCdᵤᵣ,γ the recommended value according to Ethiopian national annex is 0 mm. 🔑ΔCdᵤᵣ,st the Ethiopian national annex recommendes a value of 0 mm. 🔑ΔCdᵤᵣ,add 0 mm is recommended by Ethiopian national annex. @theoryanddesignofstructures

✔️COVER TO REINFORCEMENT ES EN 1992-1-1:2014 🔑Definition of cover according to this code is " the concrete cover is the distance between the surface of the reinforcment closest to the nearest concrete surface". ( ES EN 1992-1-1:2015 Article 4.4.1.1 ) 🔑 "The nominal cover shall be specified on drawings." ( ES EN 1992-1-1:2015 Article 4.4.1.1[2]) 🔑Cₙₒₘ=Cₘᵢₙ+ΔCdₑᵥ (ES EN 1992-1-1:2015, equation 4.1) Where :- ✅Cₙₒₘ is the nominal cover ✅Cₘᵢₙ is the minimum cover ✅ΔCdₑᵥ is allowance in design deviation. I. Minimum cover( Cₘᵢₙ ) The minimum cover shall be provided in order to ensure( ES EN 1992-1-1:2015 Article 4.4.1.2[2]) ✅ the safety transmission of bond forces ✅ the protection of the steel against corrosion. ✅ an adequate fire resistance 👉 the greater of value of Cₘᵢₙ satisfying both bond and environmental conditions shall be used ( ES EN 1992-1-1:2015 ARTICLE 4.4.1.3[2]) 🔑 Cₘᵢₙ= max {Cₘᵢₙ,b ; Cₘᵢₙ,dᵤᵣ+ΔCdᵤᵣ,γ-ΔCdᵤᵣ,st- ΔCdᵤᵣ,add; 10 mm } @theoryanddesignofstructures

the comparison between EBCS -2-1995 and ES EN 1992:2015 will continue in the near future. In order to spice up things a little bit , beam design according to ES EN 1992:2015 would be discussed here after. And let's first cover important parameters for beam design.

In Structural engineering terms what do we call መደመር? We call it the principle of superposition! As superposition makes structural calculations easier , it also helps reduce the burden our country is under!!!! Long live to Dr. Abiye

Design aid ES EN 1992-2-2:2015 design aid for sections subjected to bending with or without axial load. What we used to call design Table 1a modified according to the new code.

ES EN is the new Ethiopian code for design of concrete, steel and other structural materials and members. Starting from this year ( 2010 ) Addis Ababa municipality is requiring buildings to be designed based on ES EN and accordingly design offices are complying. And some university students are performing their final year structural engineering projects based on this code as per their advisors request. @theoryanddesignofstructures

Steel stress strain diagram