The beam shown in Fig. 1 with uniform flexural rigidity El is subjected to the two concentrated loads P. If the entire beam is modelled by one element, calculate the rotation at midspan. L/3 L/3 L L/3 Fig. 1

EXAMPLE 4.2 The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm²; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm?. For the 30-kN force shown, determine the deflection (a) of B, (b) of D, (c) of E. %3D 0.4 m 0.3 m 30 kN D E -0.4 m 0.2 m

Figure Q2(a) shows a cantilever beam that is subjected to a pure bending moment M = 3kN.m about the neutral axis (N.A) and the cross-section of a beam is shown in Figure Q2(b). Determine: (a) The moment of inertia about the neutral axis, InA. (b) The bending stress acting at point B and state whether it is in tension or compression. (c) The bending stress acting at point C (d) The maximum bending stress in the beam. M Figure Q2 (a) 20 mm B 150 mm C N 20 mm 150 mm 20 mm 250 mm Figure Q2 (b)

A rigid beam BC is suspended by rods AB and CD as shown in the figure. Rod AB is made from aluminum while rod CD is made from steel. Determine the location/ placement of the 75kN concentrated load within the beam BC such that the rigid beam BC will remain horizontal after deflection. Determine the axial deformation of rods AB and CD.

The system shown in the figure has a fixed support at A and an alumimum rod of 0.5m length at C. The beam AC is subjected to a point load of 20 kN at its midspan. In addition to that point load, alumimum rod is subjected to a temperature decrease of 25 °C. Determine the deflection and the rotation at point C. Anhunnd 70 GP in

A cantilever beam is free of support at point A and is clamped at the point B, as shown in the Figure Q4 below. Calculate the support reaction force and moment for the non-uniformly distributed load, where w =74 N/m and L = 6 m. The downward direction is denoted as positive direction in force and the anti- clockwise direction is defined as positve in moment. For all numerical answers, answer to within 3 decimal places. A v y -L- Figure Q4: A cantilever beam under non-uniformly distributed load

3. Two beams are supported as shown in the diagram below, each 150mm x 200mm x 4 meters. Beam CD is a cantilever beam carrying a uniformly distributed load of 4 KN/m freely supported on beam AB. Beam AB is freely supported on each ends. E = 13.8 GPa for both beam. Neglect the weight of the beam. a. Compute the reaction at D. b. Compute the deflection at D. c. Compute the bending stress of beam CD. 4kN Im 4m 4m

A symmetrical beam of length 300 mm is loaded with a force of 414 N downwards (positive z) and has the following equation for the vertical displacement: w (2) = - + F 48 %3D The value of E is 200,000 Nmm² and the values of ly is 20 x 10° mm“ The maximum value of z for the beam cross section is +20 mm What is the maximum tensile stress in the beam at the point when x = 86 mm?

The beam shown in the Fig.is 7m long with EI = 200MNm^2 Let P = 10 kN Determine the following: a. Reaction at A.b. Constant.c. Slope at 2m from A.d. Deflection at 2m from A.

A torque of 500 NMm is applied to the circular beam of variable radius given in the figure in the direction shown at point C. Find the support reactions at A and B points.