Chapter 5.10, Problem 242P

2. Express the following complex numbers in rectangular form. (a) z₁ = 2еjл/6 (b) Z2=-3e-jπ/4 (c) Z3 = √√√3e-j³/4 (d) z4 = − j³

A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be fixed supports. The beam was originally designed to withstand a triangular distributed load, however, the loading condition has been revised and can be approximated by a cosine function as shown in the figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can assume that the bending rigidity (El) is constant. wwo cos 2L x A B Figure 3: Built in beam with a varying distributed load In order to do this, you will: a. Solve the reaction forces and moments at point A and B. Hint: you may find it convenient to use the principal of superposition. (2%) b. Plot the shear force and bending moment diagrams and identify the maximum shear force and bending moment. (2%) c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x. (1%)

Question 1: Beam Analysis Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these moments is PL. Moment Release A B с ° MB = PL Mc= = PL -L/2- -L/2- → P D Figure 1: Two beam arrangement for question 1. To analyse this structure, you will: a) Construct the free body diagrams for the structure shown above. When constructing your FBD's you must make section cuts at point B and C. You can represent the structure as three separate beams. Following this, construct the…

A cantilevered rectangular prismatic beam has three loads applied. 10,000N in the positive x direction, 500N in the positive z direction and 750 in the negative y direction. You have been tasked with analysing the stresses at three points on the beam, a, b and c. 32mm 60mm 24mm 180mm 15mm 15mm 40mm 750N 16mm 500N x 10,000N Figure 2: Idealisation of the structure and the applied loading (right). Photograph of the new product (left). Picture sourced from amazon.com.au. To assess the design, you will: a) Determine state of stress at all points (a, b and c). These points are located on the exterior surface of the beam. Point a is located along the centreline of the beam, point b is 15mm from the centreline and point c is located on the edge of the beam. When calculating the stresses you must consider the stresses due to bending and transverse shear. Present your results in a table and ensure that your sign convention is clearly shown (and applied consistently!) (3%) b) You have identified…

7.82 Water flows from the reservoir on the left to the reservoir on the right at a rate of 16 cfs. The formula for the head losses in the pipes is h₁ = 0.02(L/D)(V²/2g). What elevation in the left reservoir is required to produce this flow? Also carefully sketch the HGL and the EGL for the system. Note: Assume the head-loss formula can be used for the smaller pipe as well as for the larger pipe. Assume α = 1.0 at all locations. Elevation = ? 200 ft 300 ft D₁ = 1.128 ft D2=1.596 ft 12 2012 Problem 7.82 Elevation = 110 ft

A closed-cycle gas turbine unit operating with maximum and minimum temperature of 760oC and 20oC has a pressure ratio of 7/1. Calculate the ideal cycle efficiency and the work ratio

Consider a steam power plant that operates on a simple, ideal Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine The thermal efficiency of the cycle,The mass flow rate of the steam and the temperature rise of the cooling water

Two reversible heat engines operate in series between a source at 600°C, and a sink at 30°C. If the engines have equal efficiencies and the first rejects 400 kJ to the second, calculate: the temperature at which heat is supplied to the second engine, The heat taken from the source; and The work done by each engine. Assume each engine operates on the Carnot cycle