Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 13, Problem 17P
To determine
The most cost-effective alternative based on equivalent annual cost by showing cash flow diagram.
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The given beam has continuous lateral support. If the live load is twice the dead load, what is the
maximum total service load, in kips / ft, that can be supported? A992 steel is used: Fy = 50 ksi,
Fu=65 ksi. Take L = 30 ft.
bf
For W40 x 149:
2tf
=
7.11,
=
=
54.3, Z 598 in.³
tw
W
W40 X 149
L
(Express your answers to three significant figures.)
a. Use LRFD.
Wtotal =
kips/ft
b. Use ASD.
Wtotal
kips/ft
The beam shown in the figure below is a W16 × 31 of A992 steel and has continuous lateral support.
The two concentrated loads are service live loads. Neglect the weight of the beam and determine
whether the beam is adequate. Suppose that P = 52 k.
For W16 × 31: d = 15.9 in., tw
=
0.275 in., h/tw = 51.6,
and M = M₁ = 203 ft-kip, Mn/₁ = Mp/α = 135 ft-kip.
P
Р
W16 x 31
a. Use LRFD.
Calculate the required moment strength, the allowable shear strength, and the maximum shear.
(Express your answers to three significant figures.)
Mu
=
OvVn
=
ft-kip
kips
kips
Vu =
Beam is -Select-
b. Use ASD.
Calculate the required moment strength, the allowable shear strength, and the maximum shear.
(Express your answers to three significant figures.)
Ma =
Vn/b
-
Va =
Beam is -Select-
ft-kip
kips
kips
Determine the smallest value of yield stress Fy, for which a W-, M-, or S-shape from the list below will
become slender.
bf/2tfh/tw
Shape
W12 × 72
8.99
22.6
W12 × 26
8.54
47.2
M4 × 6
11.9
22.0
M12 x 11.8
6.81
62.5
M6 × 4.4
5.39
47.0
S24 × 80
4.02
41.4
S10 × 35
5.03
13.4
(Express your answer to three significant figures.)
Fy
=
ksi
To which shape does this value apply?
-Select-
✓
Chapter 13 Solutions
Traffic and Highway Engineering
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- Compute the nominal shear strength of an M12 × 11.8 of A572 Grade 60 steel (Fy = 60 ksi). For M12 x 11.8: d = 12 in., tw = 0.177 in., h/tw = 62.5. Vn = kipsarrow_forwardA flexural member is fabricated from two flange plates 1/2 × 71/2 and a web plate 3/8 × 19. The yield stress of the steel is 50 ksi. a. Compute the plastic section modulus Z and the plastic moment Mp with respect to the major principal axis. (Express your answers to three significant figures.) Z = Mp = in. 3 ft-kips b. Compute the elastic section modulus S and the yield moment My with respect to the major principal axis. (Express your answers to three significant figures.) S = My = in.3 ft-kipsarrow_forward= 65 ksi. A W16×36 of A992 steel has two holes in each flange for 7/8-inch-diameter bolts. For A992 steel: Fy = 50 ksi, Fu For a W16×36: bƒ = 6.99 in., tƒ = 0.430 in., Z = 64.0 in.³ and Sx = 56.5 in.³ a. Assuming continuous lateral support, verify that the holes must be accounted for and determine the nominal flexural strength. (Express your answer to three significant figures.) Mn = ft-kips b. What is the percent reduction in strength? (Express your answer to three significant figures.) Reduction = %arrow_forward
- Find the reinforcements for the mid span and supports for an interior 9 in. thick slab (S-2) in thefloor from Problem 1. Ignore the beams and assume that the slab is supported by columns only (i.e.a flat plate). Sketch the slab and show the reinforcements including the shrinkage andtemperature reinforcement steel. Use f c’ = 4,000 psi and f y = 60,000 psi.NOTE: Problem 3 requires additional column placements at locations such as C and D. The stripof slab between these two columns will behave as a beam support to the one-way slab (with 10 ft.span). Problem 1. The figures below shows the framing plan and section of a reinforced concrete floor system.Floor beams are shown as dotted lines. The weight of the ceiling and floor finishing is 6 psf,that of the mechanical and electrical systems is 7 psf, and the weight of the partitions is 180psf. The floor live load is 105 psf. The 7 in. thick slab exterior bay (S-1) is reinforced with #5rebars @ 10 in. o.c. as the main positive…arrow_forward1- A study of freeway flow at a particular site has resulted in a calibrated speed-density relationship, as follows u = 57.5(10.008k) a) Find the free-flow speed and jam density b) Derive the equations describing flow versus speed and flow versus density c) Determine the capacity of the road 2- A rural freeway has a demand volume of 6750 v/hr. It has four 3.4 m lanes in each direction. The traffic stream is comprised of 8% heavy vehicles and a PHF of 0.94. The terrain is rolling throughout the segment. What is the level of service for the facility? What is the capacity? 3- For an urban freeway, how many 3.6 m lanes in each direction are needed to achieve LOS C on a freeway with a peak hour traffic volume of 5725 v/hr and with a PHF = 0.967 The traffic stream is comprised of 11% heavy vehicles and the location is level terrain.arrow_forwardNote: Provide a clear, step-by-step simplified handwritten solution (with no extra explanations) that is entirely produced by hand without any AI help. I require an expert-level answer, and I will assess it based on the quality and accuracy of the work, referring to the attached image for additional guidance. Make sure every detail is carefully verified for correctness before you submit. Thanks!.arrow_forward
- 3. Find the reinforcements for the mid span and supports for an interior 8 in. thick slab (S-2) in the floor from Problem 1. Ignore the beams and assume that the slab is supported by columns only. Sketch the slab and show the reinforcements including the shrinkage and temperature reinforcement steel. Use fc’ = 4,000 psi and fy = 60,000 psi.arrow_forwardProblem 4 (Apx Method) Determine (approximately) the force in each member of the truss. Assume the diagonals can support both tensile and compressive forces. 3 m 50 kN F 000 40 kN 000 000 000 000 000 000 E 000 000 000 000 000 B 3 m 20 kN D 000 000 000 000 C 3 m Problem 5 (Apx Method) Determine (approximately) the force in each member of the truss in problem 4. Assume the diagonals cannot support compressive forces.arrow_forwardThe single degree of freedom (SDOF) system the acceleration at the base (excitation) and the acceleration at the roof (response) of the SDOF system was recorded with sampling rate 50 Hz (50 samples per second, or dt= 0.02 seconds). The file ElCentro.txt includes the two columns of acceleration data. The first column lists the acceleration at the base of the SDOF system. The second column lists the acceleration at the roof of the SDOF system. (a) Plot the time histories of the recorded accelerations at the base and at the roof of the SDOF system. (b) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Central Difference method. Plot the accel- eration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed…arrow_forward
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