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23 Cards in this Set
- Front
- Back
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Forces |
Concurrent forces: forces pass through a common point Non-concurrent forces: forces that do not intersect Resultant: force that will produce the same effect on a body as two or more forces. |
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Moment |
The tendency of a force to cause rotation around a given point or axis. Measured distance from point perpendicular to force. M=(F)(d) M= moment F= force d= perpendicular distance to force from moment or axis |
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Statical moment |
The statical moment of an area with respect to an axis is defined as an area multiplied by the perpendicular distance from the centroid axis. y= AxY y= statical moment A= area Y= Distance from centroid to axis |
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Moment of inertia |
Moment of inertia = Io + (A)(y^2) Io of a rectangle= (b)(d^3)/12 |
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Stress |
Total Stress: is the total internal force in a section and is measured in pounds or Kip's Unit Stress: is the stress peer unit area if the section. 3 types of stress; tension, compression, and shear f= P/A measured in psi f= unit stress P= load A= area |
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Strain |
Strain is the deformation it change in size of a body caused by external loads. Tensile loads stretch a body and compressive loads shorten it. Total strain: total elongation it shortening if a body. Unit Strain: total strain divided by original length |
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Elastic limit |
Unit stress= P/A Unit Strain= ∆/L E= unit stress/unit strain or E=(P/A)/(∆/L) or E= PL/A(delta) or ∆= PL/AE P: load L: length A: area E: modulus of elasticity |
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Yield point |
Point where unit strain is no longer proportional to unit stress. Point where body continues to strain with no additional load added, point after the elastic limit |
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Ultimate Strength |
The ultimate strength is when the body reacts the maximum unit stress before fracture. |
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Allowable stress |
The maximum permissable unit stress, considerably lower than ultimate strength. Factor or safety: ratio between ultimate strength of material to it's working stress |
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Thermal Stress |
∆ length= nLt n= coefficient of thermal expansion L= original length t= temperature change |
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Types of beams |
Simple beam: rests on a support at really have and ends are free to rotate. Cantilever beam: supported only at one end and restrained against rotation. Overhang beam: rests on two or more supports and has one or both ends projecting beyond. Continuous beam: rests on two or more supports Fixed end beam: restrained against rotation at ends. Some are restrained at one end, free at the other. |
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Concentrated loads |
Supported at midpoint: R= P/2 Mmax= PL/2 Mx= Px/2 ∆max= P(L^2)/48EL |
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Distributed Loads |
W=wl R= wl/2 V(x)= w(1/2-x) Mmax= (w(L^2)/2)(1/2-x) Mx= Px/2 ∆max= P(L^2)/48EL |
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Vertical shear |
Vertical shear (v) at a any section is the algebraic sum of the forces that are on either side of the section. |
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Bending moment |
Bending moment (M) at any section of the been is the algebraic sum of the moment about the section on over side of the section. The bending moment is the maximum at a point where shear passes through zero. Change of moment at any two points is eaual to the area of shear between 2 points |
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Shear and moment diagrams |
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Positive and negative moments |
Simple beams: are bent concave up (+) upper gives are in compression while lower fingers after in tension. Positive moment across whole beam. Cantilever beam: bent concave down (-) top fibers in tension, bottom fibers in compression. Negative moment across beam. Overhang beam: would have both positive and negative moments across beam. Fixed beam: negative moment at ends and positive between ends |
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Flexure formula and section modulus |
f=my/I fmax= Mc/I S= I/C Fmax= M/S f= bending stress (tension or compression) M= bending moment y= distance from neutral axis c= max distance from neutral axis S= Section modulus |
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Horizontal shear stress |
v=VQ/Ib v= horizontal shear V= vertical shear Q= statical moment about neutral axis I= moment of inertia b= thickness of beam vmax occurs at neutral axis vmax= 3V/2bd |
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Deflection and Camber |
Deflection is the movement of a beam from it's original location when load is applied = ∆ Uniformly distributed load: (5/384)(wL(L^3)/EI) Concentrated load at center (PL^2)/48EI w= load per foot L= length E= modulus of elasticity I= moment of Inertia Camber is the built in curve a structural member to compensate for uniformly distributed. |
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Columns |
A column is a member primarily subject to axial compressive load. Occasionally also resists bending moments due to off centered loading (eccentricity) or perpendicular to length such as wind loads. Compressive load= P/A Flexural stress= Mc/I On compression side the maximum combined stress is compressive load + flexural stress On tension side the maximum combined stress is compressive load minus flexural strength |
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Slenderness Ratio |
Slenderness Ratio is 1/R R= radius of gyration = √I/A |
