---
title: "Indeterminacy of truss and beam-cable structure"
subject: "Theory of Structures II"
chapter: 1
key: "semester_5/theory_of_structures_ii:indeterminacy-extensible-truss-and-beam-cable"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/indeterminacy-extensible-truss-and-beam-cable
site: BCT Engineering
---

# Indeterminacy of truss and beam-cable structure

Theory of Structures II · Chapter 1: Introduction

- Asked in: 2065 Shrawan, 3+3 marks
- Video: [Lecture 4 - SA1 - Static Indeterminacy of Trusses](https://www.youtube.com/watch?v=o7sNVzF33X0) — Vyshak C
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/indeterminacy-extensible-truss-and-beam-cable
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-1

## Question

Find static and kinematic indeterminacy for the following structures with all extensible members: [Figure: (i) a truss with hinged and roller supports at the base and several internal hinges; (ii) a beam supported by cables (beam-cable system).]

## Short answer

Truss: determinate (D_s = 0), kinematic indeterminacy 13. Beam supported by cables: static indeterminacy 2, kinematic indeterminacy 9.

## Answer

All members are extensible, so $D_k$ counts all joint displacements.

#### (i) Truss with hinge and roller supports and internal hinges
Reading: a three-panel truss with top and bottom chords, four verticals and three diagonals (no redundant member). The internal hinges are pin joints of the truss and do not change the count.

$j = 8,\ m = 3 + 3 + 4 + 3 = 13,\ r = 3$

- $D_s = m + r - 2j = 13 + 3 - 16 = 0$ (determinate)
- $D_k = 2j - r = 16 - 3 = 13$

#### (ii) Beam supported by cables
Reading: a horizontal beam fixed at one end and held by two cables (tension-only bars) anchored above, attached at two points along the beam.

Unknowns: 3 fixed-end reactions + 2 cable tensions = 5. Equations = 3.

$D_s = 5 - 3 = 2$

Free beam joints: two cable-attachment points and the free end = 3 joints, each with 2 translations and 1 rotation, with the cable anchors fixed:

$D_k = 3 \times 3 = 9$

**Answer: (i) $D_s = 0$, $D_k = 13$; (ii) $D_s = 2$, $D_k = 9$.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Truss with j=8, m=13, r=3: Ds =
   A. 0
   B. 3
   C. 1
   D. 2
   Answer: A. 13 + 3 - 16 = 0, determinate. (Key point: Truss Ds)

2. With extensible members Dk = 2j - r =
   A. 16
   B. 13
   C. 19
   D. 10
   Answer: B. 16 - 3 = 13. (Key point: Truss Dk)

3. Beam fixed at one end with two cables: unknowns = 3 + 2 = 5, equations 3, so Ds is:
   A. 5
   B. 3
   C. 2
   D. 0
   Answer: C. 5 - 3 = 2. (Key point: Cable beam Ds)

4. Internal hinges of a truss change the count?
   A. Yes, add redundants
   B. Yes, subtract 1 each
   C. No, they are already pin joints
   D. Yes, double Dk
   Answer: C. Truss joints are pins, so the hinges do not alter the count. (Key point: Internal hinges in truss)

## Related in Theory of Structures II

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