PROBLEM 1 A cantilever beam of length 1.5 is loaded by concentrated force P at free end and is circular cross section (radius= 100mm), having two symmetrically placed longitudinal holes of radii R/3 with centers at R/2 above and below the neutral axis. The material is titanium alloy, having an allowable working stress in bending is 600 MPa. A) Calculate the Value of "C" in inches B) Solve for I C) Find the value of radii for both of two symmetrical placed longitudinal holes? D) Mmax? E) Pmax?

PROBLEM 1 A cantilever beam of length 1.5 is loaded by concentrated force P at free end and is circular cross section (radius= 100mm), having two symmetrically placed longitudinal holes of radii R/3 with centers at R/2 above and below the neutral axis. The material is titanium alloy, having an allowable working stress in bending is 600 MPa. A) Calculate the Value of "C" in inches B) Solve for I C) Find the value of radii for both of two symmetrical placed longitudinal holes? D) Mmax? E) Pmax?

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.2.15P: -15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide)....

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-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.
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?
The engine on the lift weighs 900 N. There are pins at points A, B, C, D, E, and G. Note, the pin at D is for the roller only as the attachment between CBD and ED is a weld. a) Determine the internal normal force, shear force and bending moment at points F and H. b) Draw the normal, shear, and bending moment diagrams for the element GAC and element CBD. c) Determine the maximum normal force, shear force and bending moment in this structure. 10° 1250 mm 500 mm | 350 mm F A C 850 mm AREAA 550 mm Н D 700 mm 1500 mm
The beam is supported by a pin at point A and a roller at point C. A distributed load is applied to the beam. Neglect the weight and thickness of the beam. Hints: 1. will need to use similar triangles to find the height after sectioning at B. 2. Review direction of normal force, shear force and bending moment and which is positive or negative. W2 W1 A di d2 Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value W1 190 N-m W2 440 N-m di 5 m d2 5 m a. Determine the magnitude of the normal force at point B, NB. . b. Determine the magnitude of the shear force at point B, VB- c. Is the shear force VB a positive or negative shear force? d. Determine the magnitude of the bending moment at point B, MB. e. Is the bending moment MB a positive or negative bending moment? Round your final answers to 3 significant digits/figures.
Problem #8: For the beam and loading shown below compute the state of stress at point B (components of the 3x3 matrix), report your answer in ksi to two decimal places. 1.5 in 1.5 in B l in F= 5 kip 3 in 1 in 15 in Fx = 4 kip 3 in Fy = 3 kip
Assignment 2 A Copper bar is loaded as shown complete the following: a. Draw a neat shear force and bending moment (Table of values is required) b. Calculate the maximum bending stress, clearly indicate where this occurs c. Calculate the maximum shear stress, clearly indicate where this occurs d. Plot the bending and shear stress for the cross section at x= 4 ft. from the left hand support. Clearly show the calculations were made at the following positions: y-0, 2, 4, 6, 8, 10 and 12 35 Ib/ft. 200 Ib Beam cross section 12 65" 8 ft. 5ft. 3 ft.
Q/ For the beams and loading shown below. A-Draw the shear force and bending-moment diagrams. B- Determine the equations of the shear force and bending-moment curves for the segments CD in Figure 2 C- Compute the bending stress at point (a) on section C. D- Determine the values and locations of the maximum tensile and compression bending stresses. Figure (2) R Point a Radius of hole: 40kN 0.5m 30 20KN/m 0.7m A B D |B 1m Im 3m Radius = R= 100 mm
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 proposed shaft is guided in rotation by two roller bearings O and C. a) Calculate T1 and T2 if T1 = 15% of T2 b) Calculate the O and C reactions. (Steps) c) Draw the diagram of the forces as well as the diagram of the bending moments D) Calculate the torsional stress of the shaft E) Calculate the bending stress of the shaft
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: The forces acting on gar- shaft- bearing system are shown in the figure given below. a) Calculate the force FR b) Find the supportreactions at O and C c) Obtain the bending moment diagrams (M, and M,) o Obtain the torque diagram (M,) e) Calculate o (bending stress) and T (torsional shea stress) at a point where the max imum bending moment is observed f) For this point, compute the principal and max imum shear stresses 400 mm 350 mm 25° 300 mm FA= 11 kN« 20° 50-mm dia. Gear A, 600-mm dia. B Gear B, 300-mm dia.
QUESTION 3 If the allowable bending stresses for a beam in one application is 6 kip/in2 in tension. The cross-section of the beam is W8 x 40. If the beam is 10 foot long and simply supported and has a concentrated load applied at x = 3 ft as shown below. • Generate the shear force and bending moment diagram in terms of P; • Based on the allowable maximum bending moment you just obtained above, calculate/ input the mazimm allowable value of the load P: please, pay attention to units, and calculate your answer to 1 decimal place.. 3 ft 7 ft kip.