Mechanics of Materials (Solid Mechanics I)

Use this for “A 16 mm bolt holds 30 kN in double shear. Find the average shear stress in it.”

Use this for “A 20 mm steel rod is stretched to a strain of 7.96 × 10⁻⁴, with ν = 0.3. How much does its diameter change?”

Use this for “A steel rod with σY = 250 MPa must carry 80 kN with a factor of safety of 2. Find its diameter.”

Use this for “A point carries σₓ = 80 MPa, σᵧ = −20 MPa and τₓᵧ = 40 MPa. Find the principal stresses, θₚ and τₘₐₓ.”

Use this for “A tank 500 mm in radius with a 10 mm wall holds 2 MPa. Find the hoop and axial stresses,” or the stress in a sphere (σₐ).

Use this for “A 1 m steel bar of 1,000 mm² held between two walls warms by 40 °C. What stress builds up, and what force does it put on the walls?”

Use this for “A bar between two walls carries 30 kN at 0.4 m from the left wall and 0.6 m from the right. Find each reaction.”

Use this for “A concrete post with 2,000 mm² of steel bars carries 1,000 kN. How much does the steel take?”

Use this for “A steel tube shaft, 60 mm outside and 40 mm inside, 1.5 m long, carries 2 kN·m. Find the largest shear stress and the twist.”

Use this for “Size a solid shaft to carry 30 kW at 1200 rpm with 60 MPa allowed.”

Use this for “A 6 m simply supported beam carries 10 kN/m. Find V and M 2 m from A, and the largest M.”

Use this for “A 100 × 200 mm beam carries a 30 kN shear force. Find the largest shear stress.”

Use this for “A beam twice as deep as it is wide carries 45 kN·m at 150 MPa allowed. Find its depth.”

Use this for “A 6 m steel beam on two supports carries 10 kN/m, with I = 80 × 10⁶ mm⁴. Does its sag stay within L ÷ 360?”

Use this for “A 2 m steel cantilever with I = 8 × 10⁶ mm⁴ carries 5 kN at its tip and 2 kN/m along it. How far does the tip drop?”

Use this for “A 2 m steel cantilever with I = 8 × 10⁶ mm⁴ carries 5 kN at its tip. How far has it dropped 1 m from the wall?”

Use this for “A pinned steel column 1.5 m long has r = 25 mm, A = 2,000 mm² and σY = 250 MPa. Find its critical stress and load.”

Use this for “A pinned steel column 5 m long has A = 2000 mm² and I = 2 × 10⁶ mm⁴. Find its slenderness ratio and critical stress. Does Euler’s formula apply if σY = 250 MPa?”

Use this for “A 50 mm solid shaft carries 20 kN of tension, a 600 N·m bending moment and an 800 N·m torque. Find the principal stresses and τₘₐₓ at the top.”

Use this for “A 150 × 300 mm post carries 120 kN pressing down 40 mm off center along the 300 mm side. Find the stress at each edge.”

Use this for “A cylinder with 100 mm inner and 125 mm outer radius holds 30 MPa inside. Find the hoop stress at the bore and compare the thin-wall value.”