After many years as a structural engineer, I realized that fundamental knowledge is essential to simplify complex calculations based on logical foundations. One must make assumptions within permissible limits (something true engineers "feel" in the data to provide reasonable boundary conditions for the problem at hand) and perform calculations using simple formulas. Naturally, the output must be "felt" once again.
A basic example is as follows: for a bending section with (1) an economical design, never use double reinforcement to resist compression, (2) only use single reinforcement for tension, (3) concrete should resist compression within allowable limits, and finally, (4) the bending section remains flat after deformation. With these four assumptions, arguing that the calculated reinforcement for bending (As) comes from the critical moment of the section (Mu) divided by the effective height after placing the reinforcement (d) will yield an equal tension/compression couple. To calculate the tension reinforcement, divide the tensile force couple (Ftu) by the design strength of the reinforcement (fyk/1.15-gamma_s), converting units to get the result in cm² for the reinforcement area. Voila, it's quite simple, isn't it?
Similarly, for shear force, assuming the inclination angle of the compression strut is 45 degrees, i.e., the cotangent of the angle is 1.0, the calculation formula for vertical shear reinforcement (Asw) parallel to the bending section at the location of maximum shear force per unit step (s) is simply the value of the critical shear force (Vu) divided by the effective height after placing the reinforcement (d), further divided by the design strength of the shear reinforcement (fywd). Cheers, the result is quite simple.
I would like to share this with young engineers who see calculations as too complex to be done by hand, so they gradually become familiar with this result to control the output of reinforced concrete design models or software.
Source: A cement and concrete industry publication.
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Arts & Métiers Engineer, Professor, Mechanical & Structural engineering, Additive Manufacturing, Data Science
1moDear ROOHOLLAH RAJABI, I couldn't download the book; would you please send it to me to the email address: m.eljai@ensam.umi.ac.ma ? Thanks a lot Best regards,