📘 structural engineering

1. **Problem Statement:** We need to find the minimum diameter $d$ of a round steel column of length $L=8$ ft, fixed at the base and pinned at the top, supporting a load $P=4.5$ ki

1. **Problem Statement:** We have a truss with joints $A, B, C, D, E, F$ and a downward load $P=7$ kN applied at joint $F$. We need to find the force in member $BD$.

1. **Problem Statement:** We are given the shear force and bending moment expressions for the segment $0 \leq x < a$ of a beam:

1. **Problem Statement:** Find the reaction forces at supports $a$, $b$, $d$, $e$, and $f$ for the given beam with multiple point loads, inclined loads, a uniform distributed load,

1. **Problem Statement:** We need to find the reaction forces at supports $a$, $b$, $d$, $e$, and $f$ for the given beam subjected to various point loads, inclined loads, a uniform

1. **Problem Statement:** Identify the Degree of Structural Indeterminacy (DSI) for each of the five given structures and interpret the results.

1. **Problem Statement:** We have a 12-ft beam AC with an 8-ft span AB and a 4-ft overhang BC.

1. **Problem Statement:** Calculate the bending stresses at the top and bottom fibers of a simply supported beam with given loads and an I-section cross-section.

1. **Problem Statement:** We have a vertical frame with joints $A$, $B$, $C$, and $D$. Loads include:

1. **Problem Statement:** We have a structural frame/beam with a $10$ kN point load, distributed loads of $5$ kN/m and $8$ kN/m, and spans of $5$ m, $8$ m, $2$ m, $3$ m, and $2$ m.

1. **Problem Statement:** We have a truss with supports at points $A$ and $E$. The truss is loaded with vertical point loads at joints $F$, $G$, $H$, and $I$. The vertical spacing

1. **Problem Statement:** Determine the force in each member of the given symmetric triangular truss subjected to the specified loads.

1. **Problem Statement:** Determine the horizontal and vertical components of the forces at points A, B, and C for the curved arch beam with given loads and dimensions.

1. **Problem Statement:** Determine the vertical reaction at the roller support, the maximum shear force, and the maximum bending moment for the beam loaded as described.

1. **Problem Statement:** We have a simply supported beam with a pin support at the left end and a roller support near the right end. The beam is loaded with a clockwise moment of

1. **Problem Statement:** Determine the force in member $BC$ of the truss under a $400$ kN downward load at joint $F$.

1. **Problem Statement:** We have a cantilever beam of length $2$ m fixed at the left end with a clockwise end moment of $220$ kN-m applied downward at the free right end. We need

1. **Problem Statement:** We have a beam with the following loads and supports:

1. **بیان مسئله:** محاسبه لنگرهای انتهایی به روش بخش‌لنگر، واکنش‌های تکیه‌گاهی و رسم دیاگرام نیروی برشی و گشتاور خمشی برای تیر افقی با بارگذاری نقطه‌ای $p+80=5+80=85$ کیلو نیوتن در

1. **بیان مسئله:** محاسبه لنگرهای انتهایی به روش پخش لنگر، واکنش‌های تکیه‌گاهی و رسم دیاگرام نیروی برشی و گشتاور خمشی برای تیر با بارگذاری نقطه‌ای $p+80$ کیلو نیوتن در نقطه B و بار

1. **State the problem:** We have a simply supported beam of length 12 m with a uniform load of 10 kN/m and two equal point loads of 150 kN each at the third points (4 m and 8 m).