A cantilever beam of rectangular cross section (width b = 25 mm. height h= 100 mm) is loaded by a force P that acts at the midheight of the beam and is inclined at an angle a to the vertical (see figure). Two strain gages are placed at point C. which also is at the midheight of the beam. Gage A measures the strain in the horizontal direction and gage B measures the strain at an angle B = 60 to the horizontal. The measured strains are e 125 x 10 and e, -375 x 10-, Determine the force P and the angle a, assuming the material is steel with E- 200 GPa and = 1/3.

A cantilever beam of rectangular cross section (width b = 25 mm. height h= 100 mm) is loaded by a force P that acts at the midheight of the beam and is inclined at an angle a to the vertical (see figure). Two strain gages are placed at point C. which also is at the midheight of the beam. Gage A measures the strain in the horizontal direction and gage B measures the strain at an angle B = 60 to the horizontal. The measured strains are e 125 x 10 and e, -375 x 10-, Determine the force P and the angle a, assuming the material is steel with E- 200 GPa and = 1/3.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.4.3P: A 4.75-in, outside diameter polyethylene pipe designed to carry chemical waste is placed in a trench...

See similar textbooks

Similar questions

A 4.75-in, outside diameter polyethylene pipe designed to carry chemical waste is placed in a trench and bent around a quarter-circular 90° bend (see figure). The bent section of the pipe is 52 ft long. Determine the maximum compressive strain If the normal strain cannot exceed 6.1 × 10-3 , what is the maximum diameter of the pipe? If d = 4.75 in., what is the minimum acceptable length of the bent section of the pipe?
The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.
A cantilever beam with a rectangular cross section (width b = 20 mm, height Ii = 175mm) is loaded by a force P that acts at the mid-height of the beam and is inclined at anangle a to the vertical (see figure). Two strain gages are placed at point C, which also isat the mid-height of the beam. Gage A measures the strain in the horizontal direction,and gage B measures the strain at an angle = 600 to the horizontal. The measuredstrainsaree A = 145 X 10_6 and 68 = —165 X lO_6.Determine the force P and the angle a, assuming the material is steel with £ = 200 GPaand v = 1/3.
The Poisson ratio formula for an auxetic structure given in the figure is given as follows:H = 8 cmL = 4 cmα = 50 °t = 5 mmThe strain value of the structure in the same direction as a result of the pull applied in the X axis from the bottom was measured as 0.26 mm / mm. Under the same loading condition:a) Calculate the strain on the Z axis of the structure.
600 strain rosette, or delta rosette, consists of three electrical-resistance strain gagesarranged as shown in the figure. Gage A measures the normal strain e, in the directionof the x axis. Gages Band C measure the strains and e in the inclined directions shown.Obtain the equations for the strains 8. e. and y, associated with the x-v axes.
Draw Mohr's circle for the following plane strain state. Then compute (or extract from your drawing) the principal strains and max shear strain. (Positive sign convention for each is shown on the figure.) Ex = 200μ, Ey=-200μ, Yxy = 50μ (rad) Ex
A steel wire with a diameter of d = 1/16 in. is bent around a cylindrical drum with aradius of R = 36 in. (see figure).a. Determine the maximum normal strain emaxb. What is the minimum acceptable radius of the drum if the maximum normalstrain must remain below yield? Assume E = 30,000 ksi and ey= 100 ksi.If R = 36 in., what is the maximum acceptable diameter of the wire if the maximumnormal strain must remain below yield?
1. Strain Gage Rosettes & Principal Stresses-The Cantilever Beam A strain gage experiment was conducted using the tungsten simple cantilever beam shown in the figure. A load was applied at end of the beam and strains from a rectangular strain gage rosette mounted on the top were recorded as follows: € = 50 με; €g = 300 με; €c = 172 με The strains are also shown in the figure. 14 in. b. Fixed End C₂ EA-50UE - E172UE ER=300μLE 12 in (Thickness = 0.125 in) 1.5 in. Load End P=6 lbs a. Reduce the rosette data and draw Mohr's strain circle. Show all three gages at their proper locations on Mohr's circle: Determine Poisson's Ratio for the beam material: Determine the elastic modulus for the beam material: Continue calculations on back of sheet or other paper if necessary, BOX YOUR ANSWERS, PLEASE!!
A circular aluminum tube of L=600mm is loaded in by compressive forces at its ends. The outside and inside diameters are 75mm and 63mm respectively. A strain gage is placed on the outside of the tube to measure nomal strains in the longitudinal direction. E=73 GPa and Poisson’s is 0.33. If the normal stress in the tube is 57 MPa, what is the load P? if the strain is 781 X 10-6, what is the shortening of the tube? What is the percent change in its cross-sectional If the tube in Problem #1 has a constant outer diameter of 75 mm along its entire length but has increased in inner diameter with a normal stress of 70 MPa over the middle third while the rest of the tube remains at 57 MPa and an additional the load of 15 kN is applied to the left at a point L/3, what is the inner diameter at the middle third if an additional load of 15kN is applied directed to the left at a point L/3 from the left, what is the inner diameter at the middle third.
The two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0, 0). After load P is applied, joint B moves to the coordinate position (0.20 in., -0.55 in.). Assume a = 9 ft, b = 6 ft, and h = 7 ft. Determine the normal strain in each bar. B P b h
The two bars shown in the figure are used to support a load P. When unloaded, joint B has coordinates (0,0). After load Pis applied, joint B moves to the coordinate position (0.40 in., -0.65 in.). Assume a = 10 ft, b = 5 ft, and h = 7 ft. Determine the normal strain in each bar. a b h B P Answers: EAB= EBC
Q.2. A braces wire is used in tension to press the teeth to P put it on their place. If the wire have a diameter of 0.03 in, initial length of l, = 10.16 cm in normal strain ɛ = 500 x 10-4 and stress o = 3000 psi. Find the elongation of the wire and load. A.