Problem 3: For the beam given below, derive the moment functions for Regions AB and BC. Use the position variables (x1 and x2) shown, with the origin at A. Provide the function, units, and the valid limits of each position variable. A 50 lb/ft 20 ft 200 lb.ft B C 10 ft

Use the Unit Load Method to compute the horizontal displacement AAX of joint A of the following planar frame. Assume that the frame has a roller support at A, a simple support at C, and that all members have same El. Express your answer as a positive EIAAX value (e.g. EIAX = 120). Drop any minus sign from your answer. C d4 El = constant C= 200 GPa I= 500(106) mm4 d1 d2 d3 Assume that W = 15 kN/m P = 10 kN d1 = 1.5 m d2 = 1.5 m d3 = 4 m d4 = 4 m The value of EIAAX is equal to:

Force P = 375 N is applied at A as shown. Find the moment about point D. Enter a positive answer if the moment is counterclockwise and a negative answer if the moment is clockwise. Note that the lengths are given in mm but the answer is asked for in N m. 100 mm- -200 mm- 200 mm 25° MD Nm D 125 mm C B

Problem 4.119 Four forces and a couple act on the beam. The vector sum of the forces is zero, and the sum of the moments about the left end of the beam is zero. What are the forces A, Ay, and B? 800 N 200 N-m Solution: The sum of the forces about the y-axis is Fx = Ay +B-800 = 0. The sum of the forces about the z-axis is = Ax = 0. The sum of the moments about the left end of the beam is ΣΜι = 11B-8(800) – 200 = 0. 800 N 200 N-m From the moments: 6600 = 600 N. 11 B = Substitute into the forces balance equation to obtain: 4 m 4 m 3m Ay = 800 - 600 = 200 N

3- Use Macaulay functions to determine the equation of the elastic curve of the beam. The beam has a flexural stiffness of El. What is the rotation of the beam at point C for the case of a = 2b? P A a B b C

A tripod shown supports a load of P = 1000 N at point A. Take note that ball and socket joints are used to mount the triopd at points B, D, and C. Consider the following:L1 = 2L2 = 4L3 = 5θ = 45°α = 30 Point C coordinates: (2, -2, 3) *Do not use Vectors in solving Determine the following: Force of AB =  __NForce of AC =  __NForce of AD =  __N

Determine the plastic moment Mp that can be supported by a beam having the cross section shown. sY = 30 ksi.