The following illustration shows an idealized crane setup for lifting large machinery. The crane'srigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a compositecolumn. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strainin the composite column should not exceed 0.1%, determine the maximum mass (in kg) ofmachinery that the crane can carry. Use r = 3 m.2rBAluminum cable:L = 2mE = 70 GPaD = 10 mmrOuter:ConcreteL = 3mE = 150 GPaDouter= 60 mmAluminum rodL = 4 mE = 70 GPaD = 25 mm2rInner core:BronzeL = 3mE = 100 GPaD = 30 mmD Solution guide:1) Analyze how the rigid bar ABCD would move due to the machinery. What kind of force willthe aluminum cable, aluminum rod, and composite column C feel due to the movement of therigid bar ABCD? Draw the FBD considering your analysis. Make sure that the forces youassumed would yield equilibrium (Not all forces are upwards/downwards; there are forcesbalancing the rotation/tilting caused by the machinery)2) Set-up the equilibrium equations. Remember the restrictions on the number of equilibriumequations in a single FBD.3) Set-up the equation for the composite.4) Considering the forces, you assumed in guide question #1, draw the deformation diagram ofthe system. Would there be a pivot point along the rigid bar? Where would it be located? Is itlocated at one of the points A, B, C, and D, or somewhere between the points? Note that if youset the pivot point in one of the points, you are assuming that the point will not go up or down; ifyou set it at B, C, or D, you are assuming that the aluminum rod, cable or the composite does notdeform and thereby experiences no force. How many compatibility equations can you formulatefrom this deformation diagram?

Given data, Maximum normal stress in the aluminium cable and aluminium rod, σmax,Al=70 MPa Maximum…

The following illustration shows an idealized crane setup for lifting large machinery. The crane's rigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a composite column. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strain in the composite column should not exceed 0.1%, determine the maximum mass (in kg) of machinery that the crane can carry. Use r = 3 m. 2r B Aluminum cable: L = 2m E = 70 GPa D = 10 mm Outer: r C Aluminum rod L = 4 m E = 70 GPa D = 25 mm 2r Inner core: D

The following illustration shows an idealized crane setup for lifting large machinery. The crane's rigid boom ABCD is supported at B by a cable, a rod pinned as D, and at C by a composite column. If the normal stress in the cable and rod should not exceed 70 MPa and the normal strain in the composite column should not exceed 0.1%, determine the maximum mass (in kg) of machinery that the crane can carry. Use r = 3 m. 2r B Aluminum cable: L = 2m E = 70 GPa D = 10 mm Outer: r C Aluminum rod L = 4 m E = 70 GPa D = 25 mm 2r Inner core: D

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.4.17P: Two separate cables AC and BC support a sign structure of weight W = 1575 lb attached to a building....

See similar textbooks

Similar questions

A spherical balloon with an outer diameter of 500 mm and thickness 0.3 mm is filled with a gas. Calculate maximum permissible pressure in the balloon if the allowable normal strain at the outer surface of the balloon is O.h Assume E = 4 MPa and v = 0,45.
Two separate cables AC and BC support a sign structure of weight W = 1575 lb attached to a building. The sign is also supported by a pin support at O and a lateral restraint in the '-direction at D. (a) Find the tension in each cable. Neglect the mass of the cables. (b) Find the average stress in each cable if the area of each cable is Ae= 0.471 in2.
A force P of 70 N is applied by a rider to thefront hand brake of a bicycle (P is the resultant of anevenly distributed pressure). As the hand brake pivots atA, a tension T develops in the 460-mm long brake cable(Ae = 1.075 mm2 ), which elongates by δ = 0.214 mm.Find the normal stress d and strain in the brake cable.
A force P of 70 N is applied by a rider to the front hand brake of a bicycle(Pis the resultant of an evenly distributed pressure). As the hand brakepivots at A. a tension T develops in the 460-mm Ions; brake cable (Ae=1.075 mm²), which elongates by δ 6=0.214 mm. Find the normal stress 8and strain e in the brake cable.Brake cable, L = 460 mmHand brake pivot A
As shown, three steel wires, each 28 mm2 in area, are used to lift a mass M. Their unstretched lengths are 19.99 m, 19.98 m, and 20 m. If M= 1,182 kg. what stress exists in the MIDDLE wire? Use E=215 Gpa. Answer must be in MPa.
The homogeneous bar ABCD shown in figure below is supported by acable that runs from A to B around the smooth peg at E, a vertical cableat C, and a smooth inclined surface at D. Determine the mass of theheaviest bar that can be supported if the stress in each cable is limitedto 100 MPa. The area of the cable AB is 250 mm2 and that of the cableat C is 300 mm2.
The 981-kg uniform bar AB is suspended from two cables AC and BD each with cross-sectional area 339 mm2. Find the location x (in mm) of P that can be safely applied to the bar if the stresses in AC and BD are limited to 119 MPa and 52 MPa, respectively. Express your answer in two decimal places.
a) Determine the tensile force T’ in the rope on the side connected to joint B: b) Determine the internal compressive normal force ƒBC in the tube BC: c) Determine the horizontal reaction force Rx and the vertical reaction force Ry in joint A: d) Determine the moment M of the center of bar AB: e) Determine the compressive stress σBC in the tube BC: f) Determine the critical load Pc for the tube BC: g) Which of the following statements about the tube BC is correct: A. The tube BC fails due to yielding B. The tube BC fails due to buckling C. The tube BC fails due to both yielding and buckling D. The tube BC is safe against both yielding and buckling h) Pin C has a diameter of 30 mm; calculate the shear stress τ of the pin C, when considering one cross-section for shear stress calculation:
Three steel plates, each 16 mm thick and width of 300 mm are joined by two 20 mm rivets as shown. Assume the rivet hole diameter = 23 mm. A. If the load P= 50 KN, determine the tensile stress of the plates. B. If the load P= 50 KN, determine the largest bearing stress acting on the rivets. C. If the ultimate shear stress for the rivets is 180 MPa, what ultimate force Pu is required to cause the rivets to fail in shear? Neglect friction between the plates.
The ring, with dimensions shown, is placed over a flexible membrane which is pumped up with a pressure p. The thickness r,-r; is small compared to r; (a) Determine the axial force F in the ring in terms of p, w and r;. Hint: Consider a FBD by cutting the ring+membrane in two. (b) Determine the hoop stress in the ring. (c) Determine the hoop strain in the ring. The modulus of elasticity for the ring is E. (d) Relate the hoop strain to the change in the inner radius of the ring after this pressure is applied, and use this to get the change in the inner radius in terms of p, E, w, r, and ri- (PLEASE ANSWER ASAP AND CORRECTLY)!
A 1.05-m-long rod of negligible weight is supported at its ends by wires A and B of equal length. The cross-sectional area of A is 1.80 mm^2 and that of B is 4.20 mm^2 . Young's modulus for wire A is 2.30×1011 Pa ; that for B is 1.20×1011 Pa . At what point along the rod should a weight w be suspended to produce equal stresses in A and B? (d=? m from wire A) At what point along the rod should a weight w be suspended to produce equal strains in A and B? (d=? m from wire A)
The heels on a pair of women's shoes have a radius of 5 cm at the bottom. If 30% of the weight of a woman 480N is supported by each heel, find the stress on each heel