Problem 1: Transformed Moment of Inertia and Elastic Deflection Given: The center of the top and bottom rebars are placed 2.5" from the top and bottom faces. Top Reinforcement: 2 no. 4 Rebar Bottom Reinforcement: 4 no. 9 Rebar Use textbook table A-1 for rebar properties Es = 29,000 ksi Ec = 3,600 ksi Unit weight of plain concrete = 145 lb/ft³ a. Find the transformed moment of inertia of the composite section. b. Calculate the reinforcement ratio p where p is Asb/bd. Asb is the area of the bottom steel, d is the depth from the top face of the beam to the bottom steel, and b is width of the beam. 16" c. A 30' simply supported beam has this cross-section. Ignoring the effects of cracking, how much would the beam deflect under its own self-weight and a live load of 0.64 kip/ft? d. Often the unit weight for reinforced concrete is assumed to be 150 lb/ft³. Repeat part c. using this assumption. e. Repeat part c. using the gross moment of inertia. Note: the gross moment of inertia is the moment of inertia assuming the beam is entirely concrete. f. Briefly discuss the difference between the deflections calculated in parts c-e. When could the simplifying assumptions made in parts d and e be useful? Are they safe assumptions to make?
Problem 1: Transformed Moment of Inertia and Elastic Deflection Given: The center of the top and bottom rebars are placed 2.5" from the top and bottom faces. Top Reinforcement: 2 no. 4 Rebar Bottom Reinforcement: 4 no. 9 Rebar Use textbook table A-1 for rebar properties Es = 29,000 ksi Ec = 3,600 ksi Unit weight of plain concrete = 145 lb/ft³ a. Find the transformed moment of inertia of the composite section. b. Calculate the reinforcement ratio p where p is Asb/bd. Asb is the area of the bottom steel, d is the depth from the top face of the beam to the bottom steel, and b is width of the beam. 16" c. A 30' simply supported beam has this cross-section. Ignoring the effects of cracking, how much would the beam deflect under its own self-weight and a live load of 0.64 kip/ft? d. Often the unit weight for reinforced concrete is assumed to be 150 lb/ft³. Repeat part c. using this assumption. e. Repeat part c. using the gross moment of inertia. Note: the gross moment of inertia is the moment of inertia assuming the beam is entirely concrete. f. Briefly discuss the difference between the deflections calculated in parts c-e. When could the simplifying assumptions made in parts d and e be useful? Are they safe assumptions to make?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Problem 1: Transformed Moment of Inertia and Elastic Deflection
Given:
The center of the top and bottom rebars are placed 2.5" from
the top and bottom faces.
Top Reinforcement: 2 no. 4 Rebar
Bottom Reinforcement: 4 no. 9 Rebar
Use textbook table A-1 for rebar properties
Es = 29,000 ksi
Ec = 3,600 ksi
Unit weight of plain concrete = 145 lb/ft³
a. Find the transformed moment of inertia of the composite section.
b. Calculate the reinforcement ratio p where p is Asb/bd. Asb is the area of the
bottom steel, d is the depth from the top face of the beam to the bottom steel,
and b is width of the beam.
16"
c. A 30' simply supported beam has this cross-section. Ignoring the effects of
cracking, how much would the beam deflect under its own self-weight and a live
load of 0.64 kip/ft?
d. Often the unit weight for reinforced concrete is assumed to be 150 lb/ft³.
Repeat part c. using this assumption.
e. Repeat part c. using the gross moment of inertia. Note: the gross moment of
inertia is the moment of inertia assuming the beam is entirely concrete.
f. Briefly discuss the difference between the deflections calculated in parts c-e.
When could the simplifying assumptions made in parts d and e be useful? Are
they safe assumptions to make?
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Step 1: Given Data
VIEWStep 2: Calculation of moment of inertia
VIEWStep 3: Calculation of moment of inertia
VIEWStep 4: Calculation of reinforcement ratio
VIEWStep 5: Calculation of deflection
VIEWStep 6: Revised eflection in the beam
VIEWStep 7: Deflection with respect to gross moment of inertia
VIEWStep 8: Percentage change in deflection
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