Statics — Quiz 3

Questions in this quiz (10)

1. A beam of length $$10\ m$$ carries a parabolic distributed load that varies from zero at both ends to a maximum of $$20\ kN/m$$ at midspan. Determine the magnitude of the resultant force.

   • $$133\ kN$$
   • $$100\ kN$$
   • $$66.7\ kN$$
   • $$80\ kN$$

2. A rectangular cross-section $$120\ mm\times80\ mm$$ has its centroid at the origin. The reference axes are rotated $$25^\circ$$ from the principal centroidal axes. Determine the product of inertia $$I_{x_1y_1}$$ about the rotated axes.

   • $$0\ mm^4$$
   • $$2.45\times10^6\ mm^4$$
   • $$1.52\times10^6\ mm^4$$
   • $$3.40\times10^6\ mm^4$$

3. A three-hinged portal frame has columns $$6\ m$$ tall and a beam $$10\ m$$ long, with hinges at both bases and at the midspan of the beam. A horizontal force of $$30\ kN$$ is applied at the beam level on the right column. Determine the horizontal reaction at the right support.

   • $$15\ kN$$
   • $$10\ kN$$
   • $$30\ kN$$
   • $$20\ kN$$

4. A force of $$500\ N$$ acts along a line from the origin $$\left(0,0\right)$$ toward point $$\left(4,3\right)$$. Determine the moment of this force about point $$\left(6,0\right)$$.

   • $$1500\ N\cdot m$$ counterclockwise
   • $$-1500\ N\cdot m$$ clockwise
   • $$2000\ N\cdot m$$ counterclockwise
   • $$1200\ N\cdot m$$ clockwise

5. A simply supported beam of length $$12\ m$$ carries a uniformly distributed load of $$5\ kN/m$$ over its entire span. Determine the location from the left support where the shear force is zero.

   • $$3\ m$$
   • $$6\ m$$
   • $$4.5\ m$$
   • $$9\ m$$

6. A parallel chord Warren truss has $$6$$ panels, each $$2.5\ m$$ long, and a height of $$2.0\ m$$. Point loads of $$10\ kN$$ are applied at each of the $$5$$ interior bottom chord joints. Determine the force in the bottom chord at the center of the truss.

   • $$25.0\ kN$$
   • $$37.5\ kN$$
   • $$56.25\ kN$$
   • $$62.5\ kN$$

7. A granular soil has an angle of repose of $$30^\circ$$. Determine the coefficient of static friction for the soil.

   • $$0.5$$
   • $$0.6$$
   • $$0.65$$
   • $$0.7$$

8. A horizontal beam of length $$10\ m$$ is supported by a pin at the left end and a roller on a surface inclined at $$45^\circ$$ at the right end. A concentrated load of $$60\ kN$$ acts at the midpoint of the beam. Determine the reaction at the roller support, measured perpendicular to the inclined surface.

   • $$30.0\ kN$$
   • $$34.6\ kN$$
   • $$42.4\ kN$$
   • $$25.0\ kN$$

9. A rigid frame consists of two vertical columns connected by a horizontal beam. When a vertical load is applied at midspan of the beam, where do points of inflection typically occur?

   • At the column bases only
   • At locations where bending moment changes sign
   • At the beam-column connections only
   • Points of inflection do not occur in rigid frames

10. A beam carries two distributed loads: a uniform load of $$4\ kN/m$$ over the first $$6\ m$$, followed by a triangular load increasing from $$0$$ to $$8\ kN/m$$ over the next $$3\ m$$. Determine the location of the resultant force measured from the left end.

    • $$4.67\ m$$
    • $$5.20\ m$$
    • $$5.85\ m$$
    • $$6.30\ m$$