Chapter 7, Problem 18QAP

Question 2 (20 points) a) In terms of n and p, how many state variables and how many inputs can you see in the system below? dx1 dt =x1- 2x2 dx2 = 3x1 - 4x2 dt b) Derive the state space representation for the above system c) Determine whether the system is stable or not.

A triangular distributed load of max intensity w acts on beam AB. The beam is supported by a pin at A and member CD, which is connected by pins at C and D respectively. Determine the largest load intensity, Wmax, that can be applied if the pin at D can support a maximum force of 18000 N. Also determine the reactions at A and C and express each answer in Cartesian components. Assume the masses of both beam and member ✓ are negligible. Dwas шал = A BY NC SA 2016 Eric Davishahl C D -a- Ур -b- X B W Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 6.6 m b 11.88 m C 4.29 m The maximum load intensity is = wmax N/m. The reaction at A is A = The reaction at C is = i+ Ĵ N. ĴN. 12 i+

The beam is supported by a pin at B and a roller at C and is subjected to the loading shown with w =110 lb/ft, and F 205 lb. a.) If M = 2,590 ft-lb, determine the support reactions at B and C. Report your answers in both Cartesian components. b.) Determine the largest magnitude of the applied couple M for which the beam is still properly supported in equilibrium with the pin and roller as shown. 2013 Michael Swanbom CC BY NC SA M ру W B⚫ C F ka b Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 3.2 ft b 6.4 ft C 3 ft a.) The reaction at B is B = The reaction at C is C = ĵ lb. i+ Ĵ lb. b.) The largest couple that can be applied is M ft-lb. == i+

The beam ABC has a mass of 79.0 kg and is supported by the rope BDC that runs through the frictionless pulley at D . The winch at C has a mass of 36.5 kg. The tension in the rope acts on the beam at points B and C and counteracts the moments due to the beam's weight (acting vertically at the midpoint of its length) and the weight of the winch (acting vertically at point C) such that the resultant moment about point A is equal to zero. Assume that rope segment CD is vertical and note that rope segment BD is NOT necessarily perpendicular to the beam. a.) Compute the tension in the rope. b.) Model the two forces the rope exerts on the beam as a single equivalent force and couple moment acting at point B. Enter your answer in Cartesian components. c.) Model the two forces the rope exerts on the beam as a single equivalent force (no couple) and determine the distance from A to the point along the beam where the equivalent force acts (measured parallel to the beam from A ). Enter your answer…

w1 Three distributed loads act on a beam as shown. The load between A and B increases linearly from 0 to a maximum intensity of w₁ = 12.8 lb/ft at point B. The load then varies linearly with a different slope to an intensity of w₂ = 17.1 lb/ft at C. The load intensity in section CD of the beam is constant at w3 10.2 lb/ft. For each load region, determine the resultant force and the location of its line of action (distance to the right of A for all cases). cc 10 BY NC SA 2016 Eric Davishahl = WI W2 W3 -b- C Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 4.50 ft b 5.85 ft с 4.28 ft The resultant load in region AB is FR₁ = lb and acts ft to the right of A. The resultant load in region BC is FR2 lb and acts = ft to the right of A. The resultant load in region CD is FR3 = lb and acts ft to the right of A.

The T-shaped structure is embedded in a concrete wall at A and subjected to the force F₁ and the force-couple system F2 1650 N and M = 1,800 N-m at the locations shown. Neglect the weight of the structure in your calculations for this problem. = a.) Compute the allowable range of magnitudes for F₁ in the direction shown if the connection at A will fail when subjected to a resultant moment with a magnitude of 920 N- m or higher. b.) Focusing on the forces and igonoring given M for now. Using the value for F1, min that you calculated in (a), replace the two forces F₁ and F2 with a single force that has equivalent effect on the structure. Specify the equivalent →> force Feq in Cartesian components and indicate the horizontal distance from point A to its line of action (note this line of action may not intersect the structure). c.) Now, model the entire force system (F1,min, F2, and M) as a single force and couple acting at the junction of the horizontal and vertical sections of the…

Stuck on the question. Please do not use AI, it will get the answer wrong.

The heated rod from Problem 3 is subject to a volumetric heating h(x) = h0 x L in units of [Wm−3], as shown in the figure below. Under the heat supply the temperature of the rod changes along x with the temperature function T (x). The temperature T (x) is governed by the d following equations: − dx (q(x)) + h(x) = 0 PDE q(x) =−k dT dx Fourier’s law of heat conduction (4) where q(x) is the heat flux through the rod and k is the (constant) thermal conductivity. Both ends of the bar are in contact with a heat reservoir at zero temperature. Determine: 1. Appropriate BCs for this physical problem. 2. The temperature function T (x). 3. The heat flux function q(x). Side Note: Please see that both ends of bar are in contact with a heat reservoir at zero temperature so the boundary condition at the right cannot be du/dx=0 because its not thermally insulated. Thank you