email and its attachment of calculation about the example of concrete beam with compression steel bars in Concrete Design Handbook, 3rd edition, which I sent to the Cement Association of Canada

 email:

about Concrete Design Handbook's Example 2.3e

Several lines omitted here.

I have some question with Example 2.3 of Concrete Design Handbook, 3rd edition, fourth printing December 2010.

In page 2-13, Example 2.3, it is assumed that the compression steel is yielding, and the moment resistance is calculated accordingly. I disagree with the assumption. I find that the compression steel does not yield, and with more compression reinforcement, compression steel's stress is getting lower and further from yielding stress. The attached is my calculation. Would you please do me a favor to give me some advice about my calculation?

Several lines omitted here.


Attachment of the email about the calculation mentioned in the email:

Concrete Design Handbook, 3rd edition, fourth printing December 2010

Page 2-13, Example 2.3 – Analysis of a Rectangular Beam with Tension and Compression Reinforcement

Calculate the flexural resistance of the beam shown in the figure.

   

d = 330mm, = 65mm, = 30MPa, fy = 400Mpa, Es = 2 X105 MPa, Ec =  4500 = 4500 = 24647 MPa

= 0.85 – 0.0015 = 0.85 – 0.0015 30 = 0.805 0.67

= 0.97 – 0.0025 30 = 0.895 0.67

= , 

= MPa

Compression force of compression rebars plus compression concrete is equal to tension force of tension rebars. Therefore,

+ =

Among above equation, is compression rebars’ area deducting the concrete area where the compression rebars occupy. is used because the elastic moduli between steel and concrete are different.  

Hence,

0.85=

0.85,

and =108.46mm is got.

= = = 324.4MPa  <  fy = 400MPa

Therefore, the compression rebars do not yield.
If there are three 30M compression rebars in this example, is calculated 282.2MPa. The trend is that with more compression rebars, becomes lower, and the compression rebars are getting further from yielding.

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