Volume of the pole
$V = \dfrac{\pi}{4}(0.3^2)(3) = 0.0675 \pi ~ \text{m}^3$
Weight of pole
$W = \gamma V = 22(0.0675 \pi) = 1.485 \pi ~ \text{kN}$
Maximum moment will occur at the base
$M = 0.1P + 3H = 0.1(25) + 3(0.95)$
$M = 5.35 ~ \text{kN} \cdot \text{m}$
Stress due to axial load
$\sigma = \dfrac{P + W}{\text{Area}} = \dfrac{(25 + 1.485 \pi)(1000)}{\frac{1}{4} \pi (300^2)}$
$\sigma = 0.4197 ~ \text{MPa}$
Bending stress at the base
$f_b = \dfrac{Mc}{I} = \dfrac{5.35(150)(1000^2)}{\frac{1}{4} \pi (150^4)}$
$f_b = 2.0183 ~ \text{MPa}$
Maximum Tensile and Compressive Stresses
$f_A = -\sigma + f_b = -0.4197 + 2.0183$
$f_A = 1.5986 ~ \text{MPa}$ ← maximum tensile stress -part (2)
$f_B = -\sigma - f_b = -0.4197 - 2.0183$
$f_B = -2.4380 ~ \text{MPa}$ ← maximum compressive stress -part (1)
Maximum Shear Stress
$V = H = 0.95 ~ \text{kN}$ ← maximum shear force
For circular cross-section
$\tau = \dfrac{4V}{3A} = \dfrac{4(0.95)(1000)}{3 \times \pi (150^2)}$
$\tau = 0.0179 ~ \text{MPa}$ ← -part (3)
