In an isolated doubly reinforced continuous T-beam of an overall depth of 600 mm, the effective cover to longitudinal steel in the web is 60 mm, and for the longitudinal steel in the flange is 50 mm. The effective depth of the beam at the mid-span and at the support sections will be _______ respectively.
- A550 mm and 550 mm
- B540 mm and 550 mmCorrect
- C550 mm and 540 mm
- D540 mm and 540 mm
Solution
Concept
Effective depth of a reinforced concrete beam is the distance from the extreme compression fibre to the centroid of the tensile reinforcement. In continuous T-beams, the position of tension reinforcement changes from bottom at mid-span to top (flange) at supports due to moment reversal.
Formula
d = Overall depth - Effective cover
Step-by-step solution
1. Understand the bending moment variation in a continuous T-beam: positive bending moment occurs at the mid-span (tension at the bottom) and negative bending moment occurs at the supports (tension at the top in the flange). 2. At the mid-span, the tension steel is located in the web with an effective cover of 60 mm. Therefore, effective depth at mid-span = 600 mm - 60 mm = 540 mm. 3. At the support, due to hogging moments, the tension steel is located in the flange with an effective cover of 50 mm. Therefore, effective depth at support = 600 mm - 50 mm = 550 mm. 4. Thus, the effective depths at mid-span and support are 540 mm and 550 mm respectively.
Why the other options are wrong
A: Fails to account for the reversal of tension steel location between mid-span and support. C: Reverses the values for mid-span and support. D: Uses the same cover for both sections ignoring structural behavior.
Shortcut
Remember that continuous beams experience moment reversal: mid-span has bottom tension (uses web cover), while support has top tension in the flange (uses flange cover).
Common mistake
blindly subtracting the web cover for both sections or mixing up the locations of tension steel for sagging and hogging moments.
Correct answer: B) 540 mm and 550 mm