The extended beam ABC in the figure below is pin-supported at A and roller-supported at B. For the given loading P=2kN A 0.5m 0.5m 0.5m M, 4 kN m
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The beam will fail if the maximum bending moment reaches 900 Nm or the maximum shear force becomes 2500 N. Is the beam safe and why?
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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.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?
- Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.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 R₂Bolts distributed about a bolt circle are often called upon to resist an external bending moment as shown in the figure. The external moment is 19 kip-in and the bolt circle has a diameter of 15 in. The neutral axis for bending is a diameter of the bolt circle. What needs to be determined is the most severe external load seen by a bolt in the assembly. M Neutral axis R NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. View the effect of the bolts as placing a line load around the bolt circle whose intensity FÅ, in pounds per inch, varies linearly with the distance from the neutral axis according to the relation Fb Fb,max R sin 8. The load on any particular bolt can be viewed as the effect of the line load over the arc associated with the bolt. For example, there are 12 bolts shown in the figure. Thus, each bolt load is assumed to be distributed on a 30° arc of the bolt circle. Under these conditions, what is the largest bolt…