CIV-10

Symmetric king-post bar force

Vertical bar of a symmetric triangular truss: N = F / (2 sin θ).

Reading speed

TrussWhipple / method of jointsEN 1993-1-1

Governing equation

N = \dfrac{F}{2\sin\theta}

where

F: Crown load (kN)
\theta: Bar inclination (°)
N: Bar force (kN)

Lecture brief

Historical brief

From Euler’s 1744 elastica and Navier’s beam theory to Mohr’s circle and transformed-section RC, structural mechanics grew as a closed-form craft before finite elements. The lab keeps those governing lines for buckling, flexure, joints and influence. This sheet (CIV-10 — Symmetric king-post bar force) is the form associated with Whipple / method of joints · EN 1993-1-1. Working symbols: $F$ , $\theta$ $\rightarrow$ $N$ . Joint equilibrium at the loaded apex of a two-bar truss resolves the load into equal chord forces F/(2 sin θ).

Purpose

Purpose: compute

N

from

F

\theta

in Structural & civil via

N = \dfrac{F}{2\sin\theta}

Vertical bar of a symmetric triangular truss: N = F / (2 sin θ). Use it when a real structural & civil question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

F = 40.000\,\mathrm{kN}

\theta = 35.000\,\mathrm{^{\circ}}

, the governing relation

N = \dfrac{F}{2\sin\theta}

yields

N = 34.869\,\mathrm{kN}

. Two identical bars, pin joints, single vertical load at the crown. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Crown load F40 kNBar inclination \theta35 °

Outputs

Bar force N34.869 kN

Reading speed

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Narration of this film

Two identical bars, pin joints, single vertical load at the crown.

Joint equilibrium at the loaded apex of a two-bar truss resolves the load into equal chord forces F/(2 sin θ).

Reading speed

Watch on YouTube