2. Consider the reinforced concrete beam shown below. It is placed in a testing frame and...

 

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2. Consider the reinforced concrete beam shown below. It is placed in a testing frame and a load, P, is gradually applied to it at midspan using a hydraulic jack. Solve using gross section properties and ignore self-weight. a) Determine the applied load, P, required to crack the beam at midspan. b) What is the curvature at midspan, cr, just before the concrete cracks? (cr = Mcr/Ectlunc) c) What is the midspan deflection just before the concrete cracks? (see pg. 1-66 of the white pages for help) d) What is the stress in the tensile steel at midspan when the applied load, P, is half of that calculated in 2a)? = 40MPa, f = 400MPa, Es = 200,000MPa, Ect = 5500f, fr = 0.6f f 4-30M Bot 3200mm 3200mm 3. For the same beam in Question 2 use the Working Stress Method of Design to determine the maximum load P that can be applied to the beam if we wish to both limit the compressive stress in the concrete to no greater than 20MPa and the tensile stress in the steel to no greater than 250MPa. Use Ec = 4500f 4. a) Repeat Question 2(a) using transformed properties b) Repeat Question 2(a) for the rectangular cross-section shown at right (which has compression steel) using transformed properties. 2-25M Top 4-30M Bot 350mm 450mm- 550mm |- 350mm 50mm 450mm 550mm 2. Consider the reinforced concrete beam shown below. It is placed in a testing frame and a load, P, is gradually applied to it at midspan using a hydraulic jack. Solve using gross section properties and ignore self-weight. a) Determine the applied load, P, required to crack the beam at midspan. b) What is the curvature at midspan, cr, just before the concrete cracks? (cr = Mcr/Ectlunc) c) What is the midspan deflection just before the concrete cracks? (see pg. 1-66 of the white pages for help) d) What is the stress in the tensile steel at midspan when the applied load, P, is half of that calculated in 2a)? = 40MPa, f = 400MPa, Es = 200,000MPa, Ect = 5500f, fr = 0.6f f 4-30M Bot 3200mm 3200mm 3. For the same beam in Question 2 use the Working Stress Method of Design to determine the maximum load P that can be applied to the beam if we wish to both limit the compressive stress in the concrete to no greater than 20MPa and the tensile stress in the steel to no greater than 250MPa. Use Ec = 4500f 4. a) Repeat Question 2(a) using transformed properties b) Repeat Question 2(a) for the rectangular cross-section shown at right (which has compression steel) using transformed properties. 2-25M Top 4-30M Bot 350mm 450mm- 550mm |- 350mm 50mm 450mm 550mm