Traffic And Highway Engineering
5th Edition
ISBN: 9781133605157
Author: Garber, Nicholas J., Hoel, Lester A.
Publisher: Cengage Learning,
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Chapter 8, Problem 24P
To determine
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10. A short column is subjected to an eccentric loading. The axial load P =
1000 kips and the eccentricity e = 12 in. The material strengths are fy = 60 ksi
and f = 6000 psi. The Young's modulus of steel is 29000 ksi.
(a) Fill in the blanks in the interaction diagram shown below.
(2pts each, 10pt total)
Po
Pn
(1)
failure range
H
3"
30"
Ast 6 No. 10 bars
=
P
22"
I
e
H
3"
(4) e =
e small
Load
path for
given e
Radial lines show constant (2)
eb
(3)
e large
failure range
Mn
(5) e=
Mo
(b) Compute the balanced failure point, i.e., P and Mb.
No chatgpt pls
11. The prestressed T beam shown below is pretensioned using low relaxation
stress-relieved Grade 270 strands. The steel area Aps = 2.5 in². The tensile
strength is fpu = 270 ksi, and the concrete compressive strength is fr =
6000 psi.
(a) Calculate the nominal moment strength Mn with hr = 6 in.
22"
15"
T
hf
(b) Since this beam is a T-beam, the nominal moment strength M₁ increases with a thicker hf. However, M, stops
increasing if he reaches a value. Determine the minimum thickness hy that can achieve the maximum nominal moment
strength Mr. Also, calculate the corresponding maximum nominal moment strength Mn with the computed hf.
Chapter 8 Solutions
Traffic And Highway Engineering
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 6PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10P
Ch. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 27PCh. 8 - Prob. 28P
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- 10. A short column is subjected to an eccentric loading. The axial load P = 1000 kips and the eccentricity e = 12 in. The material strengths are fy = 60 ksi and f = 6000 psi. The Young's modulus of steel is 29000 ksi. (a) Fill in the blanks in the interaction diagram shown below. 30" Ast 6 No. 10 bars = Pn (1) Po (4) e = e small Load path for given e failure range Radial lines show constant (2) eb (3) e large failure range Mn (5) e= Mo (b) Compute the balanced failure point, i.e., P and Mb. H 3" P 22" I e H 3"arrow_forward10. A short column is subjected to an eccentric loading. The axial load P = 1000 kips and the eccentricity e = 12 in. The material strengths are fy = 60 ksi and f = 6000 psi. The Young's modulus of steel is 29000 ksi. (a) Fill in the blanks in the interaction diagram shown below. 30" Ast 6 No. 10 bars = Pn (1) Po (4) e = e small Load path for given e failure range Radial lines show constant (2) eb (3) e large failure range Mn (5) e= Mo (b) Compute the balanced failure point, i.e., P and Mb. H 3" P 22" I e H 3"arrow_forward7. Match the given strand profiles with the corresponding loading conditions for a prestressed concrete (PSC) beam. Strand profile (b) (d) (c) (a) Ꮎ Load on a beamarrow_forward
- 4. For serviceability considerations, the effective moment of inertia (Ie) is calculated using the following formula: le 1 - 1cr ((2/3) Mcr) Ma 2 - وا ≥ Note that the upper bound was previously set as Iut in the earlier ACI equation. (a) Arrange the following moment of inertia values in ascending order (from smallest to largest): le, Ier, Ig and lut (b) Mer is the cracking moment. Choose the cross-section that should be used to compute Mcr. NA. h 5. Identify and circle the figure that represents the scenario in which the torsional effect is permitted to be reduced according to the ACI code provisions. (3 pts) mt mi B (b)arrow_forwardI will rate, thanksarrow_forward. 9. A reinforced concrete beam is subjected to V/ = 40 kips and Tu/ = 12 ft kips at the critical section. Given conditions: ⚫ Longitudinal reinforcements use No. 8 grade 60 steel with an effective depth d = 20 in. For shear capacity, V = 18 kips and V₂ = 22 kips • For transverse reinforcements, use No. 3 bars with grade 60. • The effective torsional area of A. = 150 in². • Crack angle = 45° ⚫ The minimum stirrup spacing is Smin = 4" and the maximum stirrup spacing is Smax = Find the required stirrup spacing at the critical section. 8".arrow_forward
- 3. The beam shown on the right uses three No. 8 bars made of Grade 60 steel as longitudinal reinforcement. The allowable maximum center-to-center spacing of the longitudinal rebars has been determined to be 10 inches. Now assume that Grade 80 steel will be used instead. Determine whether the beam satisfies the rebar spacing requirements according to the ACI Code. Additional assumptions: • Estimate fs = fy • 20" Clear cover: ? 12" Clear side cover: 1.5" The clear cover depth cc and the clear side cover remain unchanged, regardless of the change in material.arrow_forward6. For the slender columns shown below: a) Determine the effective buckling length factor (k) for each column. b) Circle the column with the largest buckling capacity, assuming all columns have the same length (f) and the same flexural rigidity (E+I) k = (a) (b) (c) (d)arrow_forward5. Identify and circle the figure that represents the scenario in which the torsional effect is permitted to be reduced according to the ACI code provisions. mi (a) V7+ B (b)arrow_forward
- 5. Identify and circle the figure that represents the scenario in which the torsional effect is permitted to be reduced according to the ACI code provisions. (3 pts) mi (a) V7+ B (b)arrow_forwardIf you can briefly answer each of the given questions I will rate, thanks.arrow_forwardhandwritten solution only. pls provide instructionsarrow_forward
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