Statics Quiz 1 Review Flashcards
What to do to get the RESULTANT of TWO concurrent forces?
first, arrange in tip-to-tail method;
second, use triangle laws - sin law, cosine law
in getting the resultant, get the angle, direction, and magnitude
What to do to get the RESULTANT of THREE concurrent forces?
Analytical Method
Break down the forces into their component forces
Summation of forces Rx and Ry
Use the equation R = square root of Rx squared plus Ry squared.
To get theta, Ry/Rx
Don’t forget the units and direction
What to do to get the UNKNOWN FORCES/REACTIONS of two concurrent forces in equilibrium?
Draw the FBD of the force system
Start with the FBD that only has up to TWO UNKNOWN forces.
summation of components:
Fh = zero; Fv = zero;
Equal the two solutions, then replace
You may also rearrange the forces into a triangle and then use triangle laws
What is expected of the resultant in a concurrent force system vs in a parallel force system?
concurrent - in getting the resultant, get the angle, direction, and magnitude
parallel - NO angle, get the direction, magnitude, and distance from the point ONLY.
What to do to get the RESULTANT of a parallel force system na hindi point load - magnitude, direction, distance?
Remember: no sin, cos, etc. cause THERE IS NO ANGLE
a. Get either the summation of Ry or Rx = ResultA. For sign convention, CW is pos and CCW is neg.
b. Square root of Ry squared plus Rx squared would give out the absolute value of ResultA
c. Get the distance of the resultant from the point by using Rd = summation of Fd. So the forces would be multiplied by their distance to the point.
d. Direction is based on the result
of ResultA - pos upward or neg downward.
What to do to get the RESULTANT of a parallel force system triangular, rectangular, and trapezoidal - magnitude, direction, distance?
Rectangular R = intensity or height divided by length
distance is length over two
Triangular R = one half height times length or one half bh
Distance is L/three if higher side is on the left or TwoL/three if higher side is on the right
What is the difference of a moment and a couple?
Moment, force times distance to a point
Couple, force times distance between two points
What to do to get the REACTIONS/UNKNOWN FORCES of a parallel force system in equilibrium?
Make the uniformly distributed load into a concentrated point load using the area of the triangle/rectangle/trapezoid as the resultant
Draw the FBD
- rollers have one Normal force unknown
- hinges have two
- when one force has no opposite counterpart, then it is zero. Eliminate that/them.
Summation of Ma and Mb and transposition to get the answer OR summation of M and F.
REMEMBER TO EQUATE TO ZERO TO GET THE COMPONENTS.
In case there needs a transfer, the direction of the computed reactions become opposite in the new FBD. Look at notes for clarification on this.
What is the difference between the summation of parallel moments and summation of R or F?
Summation of M = summation of magnitude times distance to the point
Summation of R or F = sum with sin, cos, or slope
Always use sign conventions! What are the sign conventions?
For concurrent forces, pos and neg depends on up and down or right and left.
For moments, couples, and parallel forces, CW for positive and CCW for negative.
How do you solve for a couple in a parallel force system?
First, you solve for a resultant. R is equal to the summation of F.
Then, solve for the distance using Rd = Fd. Solve their distance about a point.
What to do to get the RESULTANT of a nonconcurrent force system?
First, get the summation of Fh and Fv without the distance. Get R with square of Rx squared plus Ry squared. Direction is based off the signs of Rx and Ry.
Use tantheta equals Ry/Rx to get the angle.
Use Rd = FdSUM to get d.
How to solve for ix in a nonconcurrent force system?
Use Mo = Rxd + Ryd. Rx or Ry may be zero depending on if they pass through the point. Note that Mo is used and NOT Mo times d.
How to solve for the good design dam problem?
Solve for Summation of Fh and Fv.
Get the R and the angle.
Solve for Mo = Fd.
Solve for Mo = Rd.
Get d.
What to do in a couple question finding one couple and two components?
Solve first for the R either Ry or Rx, then get their distance from one another using Rd = Fd. Then, get the couple by using C = Rd.
Then use this couple to find the distance of the other couple. C = open parenthesis Bh or Ah close parenthesis times d.
What to do in the bar axial load couple problem?
Use C = Fd. That’s it.
What to do in the rollerskating point O at ankle couple problem? Finding equivalent force/magnitude and a couple system.
Sum all R.
Use Rd = Fd to get the distance of the resultant.
Use C = Rd.
What to do in a concurrent force system given the resultant nd either Rx or Ry is zero?
Keywords: Three or more concurrent, resultant parallel upwards to the y-axis, parallel positive to the x-axis, etc.
Summation of Rx or Ry is zero. Eq. A
Summation of the other Rx or Ry is the entire resultant. Eq. B
Equate both Eq. A and Eq. B to get the theta.
Substitute theta to one of the equations to get the magnitude of the force.
What to do to get the REACTIONS/UNKNOWN FORCES of a nonconcurrent force system in equilibrium? IN A TRUSS.
Just like parallel force systems, use FhSUM = zero AND FvSUM = zero AND Mo = zero. Include one unknown in the first FhSUM or FvSUM so we can compute them and we can use them on the next FhSUM or FvSUM.
