Consider a concrete beam in an interior environment as follows: a. The beam is s

Question

Consider a concrete beam in an interior environment as follows: a. The beam is simply supported with a design span of 4.8 metres. b. The dead load in the beam is uniformly distributed. c. Dead load on the beam, in addition to its own weight, is 6.9 KN/m of which 75% is permanent (long term). d. The beam carries a single concentrated live load at mid-span of 70 KN. e, 20% of the live load is considered short term. f. The dimensions of beam are: b 280 mm, d -490 mm, cover c 45 mm g. The beam only has tension reinforcement provided by 3 N20's. h. f.-25 MPa 500 MPa Ye 2 KN/m3 4 Determine: 1. The design ultimate moment in the beam M* 2. The ultimate moment capacity of the beam oMuo. Is the beam ductile? 3. The serviceability moment in the beam M 4. The bending stresses fe and f, in the beam under the serviceability moment. 5. The Code allowable mid-span deflection. 6. The long term deflection at mid-span of the beam. Does it comply with 8 the Code requirements? 7. Will this beam develop crack problems-as per the Code - at the serviceability state? If so, what is the maximum live load that the beam can carry without inducing cracks at the serviceability state? 9

Explanation / Answer

1) design span=4.8 m

Dead load=6.9 kN/m

Live load at midspan=70 kN

Maximum moment in beam due to dead load=6.9*4.8²/8=19.87 kNm

Maximum moment in beam due to live load=70*4.8/4=84 kNm

Therefore, design moment per load combination 1.2D+1.6L=1.2*19.87 + 1.6*84 =158.24 kNm

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