1- 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.

Note: 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!.

Example 3 Design a rectangular reinforced concrete beam having a 6 m simple span. A service dead load of 25 kN/m (not including the beam weight) and a service live load 10kn/m are to be supported. use f'c = 25 MPa and fy = 420MPa

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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.

Problem 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.

The 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…

Problem 2 (Using force method) Determine the force in each member of the truss. E = 29000 ksi 3 k 1.5 in² 4 ft 1.5 in² 1.5 in² 2 in² 6 k D 1.5 in² 3 ft 2 in² B