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A cantilever beam of rectangular cross section (width 6 = 25 mm, height h = 100 mm) is oaded by a force P that acts at the mid-height of the beam and is inclined at an angle a to the rertical (see figure 2). Two strain gages (instruments that measure strain along their orientation) are placed at point C, which also is at the mid-height of the beam. Gage A neasures the strain in the horizontal direction and gage B measures the strain at an angle 3 = 45°to the horizontal. The measured strains are ɛ,=125×10 and &, =-375×10 Determine the force P and the angle a , assuming the material is steel with E = 200 GPa and v =1/3.

A cantilever beam of rectangular cross section (width 6 = 25 mm, height h = 100 mm) is oaded by a force P that acts at the mid-height of the beam and is inclined at an angle a to the rertical (see figure 2). Two strain gages (instruments that measure strain along their orientation) are placed at point C, which also is at the mid-height of the beam. Gage A neasures the strain in the horizontal direction and gage B measures the strain at an angle 3 = 45°to the horizontal. The measured strains are ɛ,=125×10 and &, =-375×10 Determine the force P and the angle a , assuming the material is steel with E = 200 GPa and v =1/3.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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 mid-height of the beam and is inclined at an angle a to the vertical (see figure 2). Two strain gages (instruments that measure strain along their orientation) are placed at point C, which also is at the mid-height of the beam. Gage A measures the strain in the horizontal direction and gage B measures the strain at an angle ß = 45°to the horizontal. The measured strains are 8, =125×10° and 8, =-375x10. Determine the force P and the angle a , assuming the material is steel with E = 200 GPa and v =1/3. Figure 2: A cantilever beam is subjected to an inclined load. Hints: The normal stress in the longitudinal direction is given by the component of the force perpendicular to the cross-section divided by the area of cross-section. The shear stress on the plane is given by 21 where V is the shear force, I is the second moment of area (moment of inertia) of the cross- section, h is the height of the beam, and y is the distance from the neutral axis. Note that point C lies on the mid-height which is also the neutral axis of the beam and therefore y=0 at this point. Also note that stress due to bending moment is zero at the neutral axis.
Transcribed Image Text: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 mid-height of the beam and is inclined at an angle a to the vertical (see figure 2). Two strain gages (instruments that measure strain along their orientation) are placed at point C, which also is at the mid-height of the beam. Gage A measures the strain in the horizontal direction and gage B measures the strain at an angle ß = 45°to the horizontal. The measured strains are 8, =125×10° and 8, =-375x10. Determine the force P and the angle a , assuming the material is steel with E = 200 GPa and v =1/3. Figure 2: A cantilever beam is subjected to an inclined load. Hints: The normal stress in the longitudinal direction is given by the component of the force perpendicular to the cross-section divided by the area of cross-section. The shear stress on the plane is given by 21 where V is the shear force, I is the second moment of area (moment of inertia) of the cross- section, h is the height of the beam, and y is the distance from the neutral axis. Note that point C lies on the mid-height which is also the neutral axis of the beam and therefore y=0 at this point. Also note that stress due to bending moment is zero at the neutral axis.
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