📘 statics

1. **Énoncé du problème** : Déterminer le moment de la force de 400 lb par rapport au point A. 2. **Formule du moment** : Le moment \( M \) d'une force \( \vec{F} \) par rapport à

1. **Problem Statement:** Find the Magnitude, Direction, and Location (MDL) of the Resultant force with respect to point A for the given forces F1 to F5 acting on a rectangular fra

1. **Problem Statement:** Find the moments of inertia $I_x$ and $I_y$ about the centroidal axes for the given composite shape consisting of three rectangles and one circular hole.

1. **State the problem:** Find the magnitude, direction, and location of the resultant force with respect to point A for the given system of forces.

1. **Problem Statement:** Calculate the tension in cable BC given that the tension in cable EF is 5.0 kip and the weight of the beam is 3.5 kip.

1. **Problem Statement:** Calculate the force in cable AD given the forces in cables AB, AC, and AE, and the coordinates of points A, B, C, D, and E.

1. **Problem statement:** We have four parallel loads on a beam: three known loads and one missing load. The resultant of all four loads is 200 kN downward, located 6 m to the left

1. **Problem statement:** Determine the magnitude of the force $\vec{F}$ (in kN) such that the resultant couple moment about point A is 10 kN.m clockwise, given $\theta = 60^\circ$

1. **State the problem:** We have a crane base with two supports at points A and B. The reaction force at A, $R_A$, is given as 0. There are two downward forces: $W_c = 90.0$ kN at

1. **Problem Statement:** Calculate the reaction force $R_A$ at point A for the garbage truck with the retrieval arm extended, given forces and distances. 2. **Given Data:**

1. **State the problem:** We need to find the components of the force exerted by cable BG on the frame at point B, given the tension in cable BG is 555 N. 2. **Identify coordinates

1. **State the problem:** We have a 260-lb force applied at point A on a rolled-steel section. We want to replace this force with an equivalent force-couple system at point C.

1. **State the problem:** Calculate the moment $M_A$ about point A caused by a force $F = 12$ lb applied at an angle of $30^\circ$ to the hammer handle. 2. **Formula used:** The mo

1. **State the problem:** We have a ladder leaning against a wall with reaction forces at points A and B. Given:

1. **Problem Statement:** Find the magnitude and position of the resultant force for the beam with loads: 10 kN/m uniform distributed load, point loads 40 kN and 60 kN downward, an

1. **State the problem:** We have a truck with mass 4300 kg and a pallet of shingles with mass 1600 kg on a boom. We need to find the reaction forces at the rear wheels B and front

1. **State the problem:** We have a horizontal member pinned at point A and resting on a smooth support at B. A downward force of 60 N acts 0.5 m from A, and a counterclockwise mom

1. **Problem Statement:** Determine the support reactions at point A for the beam with a collar that can slide vertically, subjected to a 900 N downward force at the center, a 500

1. **Problem Statement:** A 300N load is applied vertically downward at point D on a semi-circular disc of radius 1.5m. We need to find the forces in cables BD and CD, and the x, y

1. **Problem Statement:** Find the magnitude and position of the resultant force for the forces 40 kN, 60 kN, 30 kN, and 20 kN acting on a beam with given positions 1, 1, 2, 3, 5.

1. **Stating the problem:** We have a 3-hinged arch with hinges at points A, S, and B. The arch is loaded with a uniformly distributed load $q = X = 1$ kN/m over the horizontal spa