16-Civ-B9 The Finite Element Method
Worked solutions to 5 past sittings (2013–2019), 16 questions. Pick a sitting, or start from a topic below.
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Moment diagrams (2 sittings): December 2016 Q2 · May 2015 Q2
- Shear (2 sittings): December 2016 Q2 · May 2015 Q2
Questions by sitting
December 2019
- Question 1: Three-bar truss with a heated member
- Question 2: Beam propped by two inclined truss bars
- Question 3: The bilinear Q4 element and a reinforced plate
December 2018
- Question 1: Reactions by virtual work, and why the element must contain the rigid body modes (Problem 1)
- Question 2: Two-span beam with a seating gap at the middle support (Problem 2)
- Question 3: Shape functions, a stiffness coefficient and consistent nodal loads for the four-node rectangle (Problem 3)
December 2016
- Question 1: Ten short questions on finite element theory
- Question 2: Beam ABCD propped by a two-bar truss — nodal displacements, shear and moment diagrams
- Question 3: Thermal stresses in a thin triangular plate modelled by one CST
May 2015
- Question 1: Ten short questions on finite element theory
- Question 2: Two-element beam — reactions and shear and moment diagrams
- Question 3: The linear triangular element — stiffness block, plate stresses and local equilibrium
May 2013
- Question 1: Copper rod in an aluminium sleeve with an initial gap
- Question 2: Rhombus plane frame with inextensible members, and the effect of a diagonal tie
- Question 3: Constant strain triangle in plane strain — element and principal stresses
- Question 4: Bilinear four-node element — strains at the centre and the hourglass mode