---
title: "Design considerations for prismatic beams"
subject: "Strength of Materials"
chapter: 9
key: "semester_4/strength_of_materials_mechanical:prismatic-beam-design-considerations"
source: https://www.bctengineer.com/q/semester_4/strength_of_materials_mechanical/prismatic-beam-design-considerations
site: BCT Engineering
---

# Design considerations for prismatic beams

Strength of Materials · Chapter 9: Design of Beams and shafts

- Asked in: year not given, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/strength_of_materials_mechanical/prismatic-beam-design-considerations
- Whole chapter: https://www.bctengineer.com/md/semester_4/strength_of_materials_mechanical/chapter-9

## Question

Explain the basic considerations in the design of prismatic beams. Distinguish between the design of beams of ductile and brittle materials, and between short and long beams. Outline the design procedure.

## Short answer

Design finds required section modulus Z = M_max / σ_all, then checks shear, principal stress, deflection and stability. Ductile materials use symmetric sections and yield stress; brittle need unsymmetric sections with larger tensile flange. Long beams are governed by bending; short beams by shear. Procedure: compute M_max, Z_req, select section, verify shear and deflection.

## Answer

A **prismatic beam** has a constant cross-section along its length. Design means choosing a section that keeps the maximum stresses within allowable limits and, where needed, the deflection within the permitted value.

#### Basic considerations
1. **Bending governs** most designs. The required section modulus is

$$
Z_{req} = \frac{M_{max}}{\sigma_{all}}
$$

2. **Shear** must be checked, especially for short, heavily loaded beams, and for thin webs: $\tau_{max} \le \tau_{all}$.
3. **Principal stresses** may be critical at points where both $\sigma$ and $\tau$ are large, such as the web-flange junction of an I-beam.
4. **Deflection** limits (for example span/325 to span/250 for many structural members) and stability against lateral buckling may govern.
5. Economy: choose the section with the least area satisfying $Z \ge Z_{req}$, with depth $>$ width so that the material is placed away from the neutral axis.

#### Ductile versus brittle materials
| Aspect | Ductile (mild steel, aluminium) | Brittle (cast iron, concrete) |
|---|---|---|
| Strength basis | Yield stress $\sigma_y$ | Ultimate stress $\sigma_u$ |
| Tension and compression | Equal | Compression much larger than tension |
| Section | Symmetrical about NA (I-section) | Unsymmetrical, bigger flange on the tension side (T or inverted T) |
| Failure criterion | Max shear stress or distortion energy | Max principal stress |

#### Short versus long beams
- **Long beams** ($L/d$ greater than about 10 to 15): bending governs; the shear stress is small.
- **Short beams** ($L/d$ small): the shear force is large relative to the moment; the shear stress, bearing at supports and web crippling may govern.

#### Design steps
1. Find reactions, draw the shear force and bending moment diagrams, get $M_{max}$ and $V_{max}$.
2. Compute $Z_{req} = M_{max}/\sigma_{all}$.
3. Select a section (standard section from tables or fix the proportions $h = 2b$ for timber).
4. Check shear stress at the NA, principal stresses at critical points, and deflection.
5. Revise the section if any check fails.

## Check yourself

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

1. How is the required section modulus found?
   A. Zreq = Mmax/σall
   B. Zreq = Vmax/τall
   C. Zreq = σall/Mmax
   D. Zreq = Mmax·σall
   Answer: A. Bending usually governs, so Z must be at least Mmax/σall. (Key point: Bending design)

2. How does section choice differ for brittle materials like cast iron?
   A. Symmetrical I-section
   B. Unsymmetrical, with the larger flange on the tension side
   C. Larger flange on the compression side
   D. Solid rectangle only
   Answer: B. Brittle materials are weaker in tension, so the NA is placed closer to the tension side. (Key point: Brittle material section)

3. What governs in a short, heavily loaded beam?
   A. Bending stress only
   B. Lateral buckling only
   C. Shear stress, bearing and web crippling
   D. Deflection under self weight only
   Answer: C. In short beams V is large relative to M. (Key point: Short versus long)

4. What follows after selecting a trial section?
   A. Compute Zreq again
   B. Fix the section without checks
   C. Check only the bending stress
   D. Check shear, principal stresses and deflection, then revise if any check fails
   Answer: D. Z is chosen for bending, then shear, principal stresses and deflection are checked. (Key point: Design procedure)

## Related in Strength of Materials

- [Derivation of shear stress formula in beams](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Abeam-shear-stress-formula-derivation) — Strength of Materials, chapter 5
- [Shear stress in rectangular and circular beams](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Ashear-distribution-rectangle-circle-ratio) — Strength of Materials, chapter 5
- [Design of a timber beam](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Atimber-beam-design-udl-point-load) — Strength of Materials, chapter 9
- [Stress-strain diagram of mild steel](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Astress-strain-diagram-mild-steel) — Strength of Materials, chapter 2
- [Elongation of tapered bar and self-weight](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Atapered-bar-elongation-derivation) — Strength of Materials, chapter 2

## Related in other subjects

- [Ductile versus brittle failure](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aductile-brittle-failure) — Civil Engineering Materials, chapter 1
- [Ductile and brittle stress-strain behaviour](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Aductile-vs-brittle-stress-strain) — Material Science, chapter 3
- [Ductile detailing of beams and columns](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aductile-detailing-of-beams-and-columns) — Design of RCC Structure, chapter 12, asked 2×
- [Ductile design per IS 13920, beam and column](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aductile-design-per-is-13920-beam) — Design of RCC Structure, chapter 12