📘 structural engineering

1. The problem is to understand and apply the method of joints to analyze trusses. 2. The method of joints involves isolating each joint in a truss and applying the equilibrium equ

1. **Problem Statement:** Calculate the support reactions, draw the shear force diagram, and draw the bending moment diagram for a beam with the following data:

1. مسئله: ترسیم دیاگرام شکل پذیری ستون AB و تعیین معیار پذیرش برای حد ایمنی جانبی در صورت‌زیه با توجه به بار محوری 120 تن و مشخصات داده شده. 2. داده‌ها و پارامترها:

1. **Problem Statement:** Determine the axial force on member DE in kiloNewtons using the cantilever method.

1. **Stating the problem:** We have a rectangular frame with vertical height $h=4$ m and horizontal length $b=a=6$ m.

1. **State the problem:** We need to draw the shear force and bending moment diagrams for a beam with the following loads and supports:

1. **Problem Statement:** Calculate the vertical deflection at point U on a simply supported beam with two downward point loads each of magnitude $\frac{P}{2}$ applied at points T

1. **Problem Statement:** We need to draw the shear and moment diagrams for a compound beam ABC with a pin at B.

1. **Problem Statement:** Determine the end shear forces and end moments for a beam subjected to a distributed load of 540 lb/ft along the hypotenuse of a right triangle with legs

1. **Problem Statement:** Using the method of sections, determine the forces in members DE, DH, and IH of the given truss.

1. **Problem Statement:** Calculate the nominal axial load strength $P_n$ and nominal shear capacities along x and y directions for a rectangular column with given dimensions and m

1. **Problem Statement:** Calculate the nominal axial load strength $P_n$ of a rectangular column with dimensions $W=400$ mm and $L=600$ mm, concrete compressive strength $f'_c=28$

1. **Problem Statement:** Calculate the nominal axial load strength $P_n$ and nominal shear capacities along the x- and y-directions for a rectangular reinforced concrete column wi

1. **Problem Statement:** Calculate the slope and deflection at point A of a cantilever beam with a moment load of 75 klb·ft at A and a uniformly distributed load of 3.5 klb/ft ove

1. **Problem Statement:** Analyze the simply supported steel beam of span $L=6.0$ m under a uniformly distributed load (UDL) $w=3.0$ kN/m and a concentrated load $P=10.0$ kN at mid

1. The problem is to understand and interpret the inequality $h/tw > 2.24 \sqrt{E/f_y}$. 2. This inequality relates the slenderness ratio $h/tw$ of a structural element to material

1. **Problem Statement:** We need to find the eigenvalues and eigenvectors of the stiffness matrix $$K = \begin{bmatrix} k_x & 0 \\ 0 & k_y \end{bmatrix}$$ where $$k_x = k_y = \fra

1. **Problem Statement:** Analyze the given truss structure with points A, B, C, D, and E, each segment 1 m long, total length 4 m. Loads of 10 kN act downward at B, C, and D. Supp

1. **Problem Statement:** Calculate various moments and strengths for a rectangular reinforced concrete beam with given dimensions and material properties.

1. **Problem Statement:** Calculate the forces in members CF, CG, and EF of the loaded truss given the external loads and geometry. 2. **Relevant Formulas and Concepts:**

1. **Problem Statement:** Determine the forces in members BD, BE, and CE of the given truss using the method of sections.