A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria). (a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.
A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria). (a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.
Solution Summary: The author explains the orientation of the neutral axis and the maximum tensile and compressive stress.
A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria).
(a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress
(b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
I had a theoretical question about attitude determination. In the attached images, I gave two axis and angles. The coefficient of the axes are the same and the angles are the same. The only difference is the vector basis. Lets say there is a rotation going from n hat to b hat. Then, you introduce a intermediate rotation s hat. So, I want to know if the DCM produced from both axis and angles will be the same or not. Does the vector basis affect the numerical value of the DCM? The DCM formula only cares about the coefficient of the axis and the angle. So, they should be the same right?
3-15. A small fixed tube is shaped in the form of a vertical helix of radius a
and helix angle y, that is, the tube always makes an angle y with the horizontal.
A particle of mass m slides down the tube under the action of gravity. If there is
a coefficient of friction μ between the tube and the particle, what is the steady-state
speed of the particle? Let y
γ
30° and assume that µ < 1/√3.
Chapter 6 Solutions
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