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238 Finding the resultant of trapezoidal loading

Problem 238
The beam AB in Fig. P-238 supports a load which varies an intensity of 220 N/m to 890 N/m. Calculate the magnitude and position of the resultant load.
 

Simple beam with trapezoidal load over the entire span

 

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237 Finding the resultant of parallel forces acting on both sides of the rocker arm

Problem 237
Determine the resultant of the four parallel forces acting on the rocker arm of Fig. P-237.
 

Parallel forces acting on the rocker arm

 

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236 Computation of the resultant of parallel forces acting on the lever

Problem 236
A parallel force system acts on the lever shown in Fig. P-236. Determine the magnitude and position of the resultant.
 

Parallel forces acting on the lever

 

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233 A force creating counterclockwise and clockwise moments

Problem 233
In Fig. P-231, a force P intersects the X axis at 4 ft to the right of O. If its moment about A is 170 ft·lb counterclockwise and its moment about B is 40 ft·lb clockwise, determine its y intercept.
 

Three points in XY plane (A, B, and O)

 

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232 Moment of a force about points O and B

Problem 232
In Fig. P-231, the moment of a certain force F is 180 ft·lb clockwise about O and 90 ft·lb counterclockwise about B. If its moment about A is zero, determine the force.
 

Three points in XY plane (A, B, and O)

 

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231 Force P producing a clockwise moment about the origin

Problem 231
A force P passing through points A and B in Fig. P-231 has a clockwise moment of 300 ft-lb about O. Compute the value of P.
 

Three points in XY plane (A, B, and O)

 

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230 Distance from truss member to truss joint

Problem 230
For the truss shown in Fig. P-230, compute the perpendicular distance from E and from G to the line BD. Hint: Imagine a force F directed along BD and compute its moment in terms of its components about E and about G. Then equate these results to the definition of moment M = Fd to compute the required perpendicular distances.
 

Symmetrical Truss

 

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229 Y-coordinate of the point of application of the force

Problem 229
In Fig. P-229, find the y-coordinate of point A so that the 361-lb force will have a clockwise moment of 400 ft-lb about O. Also determine the X and Y intercepts of the line of action of the force.
 

Point of application of a force

 

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Example 03 | The General Power Formula

Problem
Integrate $\displaystyle \int \dfrac{dx}{\sqrt[7]{x^2}}$.
 

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Example 02 | The General Power Formula

Problem
Evaluate $\displaystyle \int \sqrt{ax + b} ~ dx$.
 

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