Structural Mechanics and Digital Communication Exercises

Posted on Apr 29, 2026 in Civil Engineering

Shear Stress in Beam Sections

  • 16.1: Rectangular beam (b = 100 mm, d = 250 mm, L = 3 m, w = 40 kN/m). Find the maximum shear stress (τmax) and its distribution.
  • 16.2: Triangular section (b = 100 mm, h = 150 mm, F = 13.5 kN). Find the maximum shear stress (τmax) and its distribution.
  • 16.3: Circular section (d = 100 mm, F = 30 kN). Find the maximum shear stress (τmax) and its distribution.
  • 16.4: I-section (Flange = 150 × 20 mm, Web = 300 × 10 mm, F = 50 kN). Find the maximum shear stress (τmax).
  • 16.5: I-section (D = 350 mm, B = 200 mm, web = 12.5 mm, flange = 25 mm, F = 200 kN). Determine the shear stress distribution.
  • 16.6: T-section (F = 100 kN, I = 113.4 × 106 mm4). Calculate shear at specific points and the distribution.
  • 16.7: Unequal I-section (σc = 17.5 MPa, F = 100 kN). Determine the bending moment and shear distribution.
  • 16.8: Irregular section (F = 20 kN). Calculate shear at specific points and the distribution.
  • 16.9: Square section (diagonal orientation): Diagonal = 2b, shear force = F. Find the maximum shear stress (τmax) and its distribution.
  • 16.10: Rolled Steel Joist (RSJ): D = 200 mm, B = 160 mm, tf = 22 mm, web = 12 mm. Determine the shear share between the flange and the web.

Torsion of Shafts and Power Transmission

  • 27.1: Solid shaft (D = 50 mm, τ = 40 MPa). Find the torque.
  • 27.2: Solid shaft (T = 10 kN·m, τ = 45 MPa). Find the required diameter.
  • 27.3: Hollow shaft (D = 80 mm, d = 50 mm, τ = 45 MPa). Find the torque.
  • 27.4: Solid shaft (D = 60 mm, N = 150 rpm, τ = 50 MPa). Find the power.
  • 27.5: Hollow shaft (D = 100 mm, d = 40 mm, N = 120 rpm, τ = 50 MPa). Find the power.
  • 27.6: Solid shaft (D = 100 mm, P = 120 kW, N = 150 rpm). Find the shear stress.
  • 27.7: Hollow shaft (P = 200 kW, N = 80 rpm, τ = 60 MPa, d = 0.6D). Find the internal and external diameters.
  • 27.8: Solid shaft (P = 100 kW, N = 160 rpm, τ = 70 MPa, Tmax = 1.2T). Find the diameter.
  • 27.9: Solid shaft (D = 125 mm, θ = 1°, L = 1.5 m, C = 70 GPa). Find the torque.
  • 27.10: Hollow shaft (D = 100 mm, d = 60 mm, τ = 35 MPa, C = 85 GPa). Find the angle of twist.
  • 27.11: Solid shaft (D = 120 mm, P = 200 kW, N = 100 rpm, θ = 2°, C = 90 GPa). Find the length.
  • 27.12: Solid shaft (D = 80 mm, θ = 1.5°, L = 5 m, τ = 42 MPa, C = 84 GPa). Find the maximum torque based on both strength and stiffness conditions.
  • 27.13: Solid shaft (T = 1.6 kN·m, τ = 60 MPa, θ = 1° per 20D, C = 80 GPa). Find the diameter.
  • 27.14: Solid vs. Hollow Shafts: Solid (D = 200 mm) and hollow (d = 150 mm) with the same area. Find (a) the power ratio and (b) the twist ratio.
  • 27.15: Shaft Replacement: Solid (D = 60 mm) replaced by a hollow shaft (d = 0.5D). Find the hollow diameters and material saving.
  • 27.16: Shaft Replacement: Solid (D = 80 mm) replaced by a hollow shaft (D = 100 mm). Find the internal diameter.
  • 27.17: Shaft Replacement: Solid Aluminum (D = 50 mm) vs. Hollow Steel (same D, C1 = 28 GPa, C2 = 85 GPa). Find the internal diameter.
  • 27.18: Hollow vs. Solid: Hollow (D = 300 mm, d = 200 mm, Cs = 2.4 Ca). Find the solid diameter and the rigidity ratio.

Digital Communication and Signal Processing

Sampling and Quantization

  • Q1: State and explain the Sampling Theorem. Derive the Nyquist rate.
  • Q2: Define sampling frequency, Nyquist rate, and Nyquist interval with relevant examples.
  • Q3: A signal with a bandwidth of 5 kHz is sampled. Find (a) the minimum sampling frequency and (b) the Nyquist interval.
  • Q4: A 2 kHz signal is sampled using PCM with 8 bits per sample. Find (a) the bit rate and (b) the required bandwidth.
  • Q5: Explain Pulse Code Modulation (PCM) using a detailed block diagram.
  • Q6: Define quantization and explain the concept of quantization error.
  • Q7: A 3 kHz signal is encoded using 4-bit PCM. Find (a) the sampling rate, (b) the bit rate, and (c) the bandwidth.

Modulation Techniques and Detection

  • Q8: Explain ASK, FSK, and PSK modulation techniques with their respective waveforms.
  • Q9: Compare BPSK and QPSK in terms of bandwidth efficiency and performance.
  • Q10: Differentiate between coherent and non-coherent detection methods.
  • Q11: A 3 kHz signal is encoded using 4-bit PCM. Find (a) the sampling rate, (b) the bit rate, and (c) the bandwidth.
  • Q12: A 1 kHz input signal is sampled at 25% above the Nyquist rate in a 12-bit PCM system. Find the required bandwidth and total bits transmitted.
  • Q13: Explain QPSK modulation and demodulation using a block diagram.
  • Q14: Explain Quadrature Amplitude Modulation (QAM) and its primary advantages.