The extended beam ABC in the figure below is pin-supported at A and roller-supported at B. For the given loading P 2kN 0.5m 0.5m 0.5m M=4 kN m
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Plot the shear force diagram of the beam
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- Solve the preceding problem using the following data: beam cross section is 100 x 150 mm, length is 3 m, and point load is P = 5 kN at mid-span, Point C is located 25 mm below the top of the beam and 0.5 m to the right of support A.Repeat Problem 6.2-1 but now assume that the steel plate is smaller (0.5 in. × 5 in.) and is aligned with the top of the beam as shown in the figure.Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.
- Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?In the given figure, support A is a roller and support B is a pin support. If P=15 kips, calculate the 1) vertical reaction at A, 2) vertical reaction at B, 3) horizontal reaction at B P 6 kips 6 kips В 6 ft – 3 ft 2 ft ' 2 ft
- Homework -3- Q1: A simply supported beam as shown in figure (1-A) below, having an I-cross section, has an over all width 200 mm and all depth 300 mm with flanges and web of thickness 20 mm shown in figure (1-B). (a) Draw the shear force and bending moment diagrams of the beam; (b) Determine the maximum compression and tension bending stress which can setup in the beam. 25 20 kN 20 kN 10 kN 150 60 kN/m (All dimensions in mm) 30 kN/m 100 1.5 m Im Im Im 50 50 50 50 50 Figure (1-A) Figure (1-B) Q2: A simply supported beam AB has a length of 3 m and carries distributed load which varies in linear manner from (1w) N/m at A support to (2w) N/m at the B support and concentrated load (1.5w) N at 2 m from A support, and the beam has hollow circular cross section of diameter ratio dindout =1/3. Draw S.F. and B.M. diagrams for the beam and determine the value of (w) if the maximum bending stress 110 N/mm?, and the average shear stress at 1 m from point A equal to 15 N/mm?.The figure Q3 below shows a bolt holding together two components. The bolt has a loadbearing diameter of 6mm and a pitch of 1mm. It is made from steel with E=210 GPa. It istightened 5 degrees beyond normal contact. The hole it passes through is 8mm diameter andits clamping force is distributed to a diameter of 16mm.a) Determine an equation for the deflection of the bolt when in contact with component 1and component 2 as function of axial load? b) Write an equation for the deformation of component 1 in contact with both the bolt andcomponent 2 as a function of axial loading. c) Present an equation for the deflection of component 2 in contact with both component 1and the bolt as a function of axial loading.d) Establish a compatibility relationship for the deformation of structure in Fig. 3 e) Determine the force being exerted on component 1 and component 21) Ball bearings support the rotating axle shown below at points A and D. The rotating axle is loaded by a stationary (non-rotating) force of F = 6.8 kN. In the drawing below, all dimensions are in mm. While the real part has fillets (r=3mm), you can assume an abrupt change in geometry for each shaft step for this problem. The axle is machined from AISI cold-drawn steel with an ultimate strength of S_u = 690 MPa, a yield strength of S_y=580 MPa, and a modulus of Elasticity of E_steel = 207 GPa. Determine the displacement at the 6.8 kN load and points B and C. 6.8 KN 30 10 250 32 B 75 38 100 10-1 -35 30
- 4-67. Figure P4-67 shows a shaft carrying three gears that rotates at 1150 rpm. Gear A delivers 20 kW to a mat- ing gear that drives a mixer. Gear C delivers 12 kW to a different mating gear that drives a circular saw. All power comes into the shaft through gear B. Consider- ing only torsion, compute the shearing stress in each part of the shaft. Consider stress concentrations.For the beam stated in P3-31, compute the maximum stress due to bending and the maximum vertical shear stress if it has a solid circular section. Objective: Omax =?, Vertical Tmax =? R₁ 3 ft 1200 lb 4 ft Ap=D2/8 Q = A₂9 1200 lb 0.212D =ỹ -X D 3 ft R₂A part of the structure for a facory automation system is a beam that spans 30.0 inches as shown below. Loads that are applied at two points each 8.0inches from a support. The left load F1=1800 lb remains constantly applied while the right load F2=1800 lb is applied and removed frequently as the machine cycles. Find the following: Maximum stress Minimum stress Mean stress Alternating stress Stress ratio Solve the missing parameters in complete solution put necessary diagrams if needed. Thanks