4.17. A rectangular beam made using concrete with f c ′ = 6000 psi and steel with f y = 60,000 psi has a width b = 20 in., an effective depth of d = 17.5 in., and a total depth of h = 20 in. The concrete modulus of rupture f r = 530 psi. The elastic moduli of the concrete and steel are, respectively, E c = 4,030,000 psi and E s = 29,000,000 psi. The tensile steel consists of four No. 11 (No. 36) bars. ( a ) Find the maximum service load moment that can be resisted without stressing the concrete above 0 .45 f c′ or the steel above 0.40 f y . ( b ) Determine whether the beam will crack before reaching the service load. ( c ) Compute the nominal flexural strength of the beam. ( d ) Compute the ratio of the nominal flexural strength of the beam to the maximum service load moment, and compare your findings to the ACI load factors and strength reduction factor.
4.17. A rectangular beam made using concrete with f c ′ = 6000 psi and steel with f y = 60,000 psi has a width b = 20 in., an effective depth of d = 17.5 in., and a total depth of h = 20 in. The concrete modulus of rupture f r = 530 psi. The elastic moduli of the concrete and steel are, respectively, E c = 4,030,000 psi and E s = 29,000,000 psi. The tensile steel consists of four No. 11 (No. 36) bars. ( a ) Find the maximum service load moment that can be resisted without stressing the concrete above 0 .45 f c′ or the steel above 0.40 f y . ( b ) Determine whether the beam will crack before reaching the service load. ( c ) Compute the nominal flexural strength of the beam. ( d ) Compute the ratio of the nominal flexural strength of the beam to the maximum service load moment, and compare your findings to the ACI load factors and strength reduction factor.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
4.17. A rectangular beam made using concrete with f c ′ = 6000 psi and steel with
f y = 60,000 psi has a width b = 20 in., an effective depth of d = 17.5 in., and
a total depth of h = 20 in. The concrete modulus of rupture f r = 530 psi. The
elastic moduli of the concrete and steel are, respectively, E c = 4,030,000 psi
and E s = 29,000,000 psi. The tensile steel consists of four No. 11 (No. 36) bars.
( a ) Find the maximum service load moment that can be resisted without
stressing the concrete above 0 .45 f c′ or the steel above 0.40 f y .
( b ) Determine whether the beam will crack before reaching the service load.
( c ) Compute the nominal flexural strength of the beam.
( d ) Compute the ratio of the nominal flexural strength of the beam to the maximum
service load moment, and compare your findings to the ACI load
factors and strength reduction factor.
Transcribed Image Text:-28"-
36"
36"
4"
2-2"
24"
typ
36"
36"
2-2"
typ
8"
(a) f
= 4000 psi
(b) f
= 5000 psi
(c) = 6000 psi
(d) f
= 3000 psi
%3D
FIGURE P4.1
Transcribed Image Text:4.16. Determine the required area of reinforcement and the corresponding rein-
forcement ratio for the section in Fig P4.1d if the ultimate moment is (a)
10,000 in-kips and (b) 5000 in-kips. f, = 60,000 psi. Comment on your solutions.
4.17. A rectangular beam made using concrete with f.
= 6000 psi and steel with
f, = 60,000 psi has a width b = 20 in., an effective depth of d = 17.5 in., and
a total depth of h
elastic moduli of the concrete and steel are, respectively, E.
and E = 29,000,000 psi. The tensile steel consists of four No. 11 (No. 36) bars.
(a) Find the maximum service load moment that can be resisted without
stressing the concrete above 0.45f or the steel above 0.40f.
(b) Determine whether the beam will crack before reaching the service load.
(c) Compute the nominal flexural strength of the beam.
(d) Compute the ratio of the nominal flexural strength of the beam to the max-
imum service load moment, and compare your findings to the ACI load
factors and strength reduction factor.
20 in. The concrete modulus of rupture f, = 530 psi. The
4,030,000 psi
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Step 1: Convert the unit of elastic modulus from psi to ksi using the formula;
VIEWStep 2: Determine the compressive strength fc of concrete using the formula;
VIEWStep 3: Determine the constant value k using the formula;
VIEWStep 4: Determine the moment due to concrete using the formula;
VIEWStep 5: Determine the moment of inertia of the beam;
VIEWStep 6: Determine the change in depth of the beam c using the relation;
VIEWStep 7: Determine the critical moment for cracked transformed section;
VIEWStep 8: Determine the stress block depth (a) using the relation;
VIEWStep 9: Determine the ratio of nominal capacity of the beam & maximum service level capacity;
VIEW
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